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The Lorenz curve is used to describe the relationship between the cumulative proportion of household income and the number of households of an economy. The extent to which the Lorenz curve deviates from the line of equality (i.e., y = x) is quantified by the Gini coefficient. Prior models are based on the simulated and empirical data of income distributions. In biology, the Lorenz curves of cell or organ size distributions tend to have similar shapes. When the Lorenz curve is rotated by 135 degrees counterclockwise and shifted to the right by a distance of 2 , a three-parameter performance equation (PE), and its generalized version with five parameters (GPE), accurately describe this rotated and right-shifted curve. However, in prior studies, PE and GPE were not compared with the other Lorenz equations, and little is known about whether the skewness of the distribution could influence the validity of these equations. To address these two issues, simulation data from the beta distributions with different skewness values and six empirical datasets of plant (organ) size distributions were used to compare PE and GPE with three other Lorenz equations in describing the rotated and right-shifted plant (organ) size distributions. The root-mean-square error and Akaike information criterion were used to assess the validity of the two performance equations and the three other Lorenz equations. PE and GPE were both validated in describing the rotated and right-shifted simulation and empirical data of plant (organ) distributions. Nevertheless, GPE worked better than PE and the three other Lorenz equations from the perspectives of the goodness of fit, and the trade-off between the goodness of fit and the model structural complexity. Analyses indicate that GPE provides a powerful tool for quantifying size distributions across a broad spectrum of organic entities and can be used in a variety of ecological and evolutionary applications. Even for the simulation data from hypothetical extreme skewed distribution curves, GPE still worked well. [ABSTRACT FROM AUTHOR]

Universal health coverage relies on providing essential medical services and shielding individuals from financial risks. Our study assesses the progressivity of out-of-pocket (OOP) payments, identifies factors contributing to healthcare expenditure inequality, and examines catastrophic health expenditures (CHE) prevalence in Kazakhstan from 2018 to 2021. Using retrospective analysis of National Statistics Bureau data, we employed STATA 13 version for calculations CHE incidence, progressivity, Lorenz and concentration curves. In 2020–2021, OOP expenditures in Kazakhstan decreased, reflecting a nearly twofold reduction in the CHE incidence to 1.32% and 1.24%, respectively. However, during these years, we observe a transition towards a positive trend in the Kakwani index to 0.003 and 0.005, respectively, which may be explained by household size and education level factors. Increased state financing and quarantine measures contributed to reduced OOP payments. Despite a low healthcare expenditure share in gross domestic product, Kazakhstan exhibits a relatively high private healthcare spending proportion. The low CHE incidence and proportional expenditure system suggest private payments do not significantly impact financial resilience, prompting considerations about the role of government funding and social health insurance in the financing structure. [ABSTRACT FROM AUTHOR]

Indoor air quality and respiratory health have always been an area of prime interest across the globe. The significance of low-cost air quality sensing and indoor public health practices spiked during the pandemic when indoor air pollution became a threat to living beings, especially human beings. Problem Definition: Indoor respiration-associated diseases are hard to diagnose if they are due to indoor environmental conditions. A major challenge was observed in establishing a baseline between indoor air quality sensors and associated respiratory diseases. Methods: In this work, 10,000+ articles from top literature databases were reviewed using six bibliometric analysis methods (Lorenz Curve of Citations, Hirch's H-Index, Kosmulski's H2-Index, Harzing's Hl-Norm-Index, Sidoropolous's HC-Index, and Schrieber's HM-index) to formulate indoor air quality sensor and disease correlation publication rubrics to critically review 482 articles. Results: A set of 152 articles was found based on systematic review parameters in six bibliometric indices for publications that used WHO, NIH, US EPA, CDC, and FDA-defined principles. Five major respiratory diseases were found to be causing major death toll (up to 32%) due to five key pollutants, measured by 30+ low-cost sensors and further optimized by seven calibration systems for seven practical parameters tailored to respiratory disease baselines evaluated through 10 cost parameters. Impact: This review was conducted to assist end-users, public health facilities, state agencies, researchers, scientists, and air quality protection agencies. [ABSTRACT FROM AUTHOR]

As an on-demand mobility service, parking reservations can greatly alleviate the issue of parking challenges. There are currently three primary strategies for parking reservation: first-come-first-served, permit reservation, and auction. In contrast to the first-come-first-served and permit-reserved strategies, the auction strategy uses dynamic pricing to allocate parking supplies efficiently based on the auction, which attracts more scholars for the research. However, parking reservations based on the auction process may have an inequity issue because drivers' age, gender, income level, and location of residence fluctuate. This inequity may limit the growth of reserved parking by influencing parking drivers' acceptance of reserved parking. But currently, very few scholars focus on the issue of reserved parking equity, and even fewer measure this nebulous and personal issue. In consideration of this, the Lorenz curve of parking reservation and the vertical equity index of parking reservation are proposed in this paper along with the calculation method for the index, which enables the problem of reserved parking vertical equity to be visualized and made concrete. The numerical experimental method is used to analyze the vertical equity of drivers with varying income levels, utilizing the Vickrey–Clarke–Groves (VCG) auction process as an example. According to the research, loss-averse drivers are more than gain-neutral and gain-seeking drivers when the income levels of the drivers using reserved parking are the same. With the increasing number of high-income drivers involved in the parking reservation, medium to low-income drivers would lose their chances of successful reservations because of their uncompetitive bid price which leads to inequity issues when the number is less than the number of parking spaces. In contrast, the vertical equity index changes more for gain-seeking drivers while being generally steady when loss-averse and gain-neutral drivers participate. For instance, when the profit and loss coefficient is 3 and 15% of drivers with high-income levels use the parking reservation platform, the vertical equity index rises from 0.09128 to 0.45434. The reference price has a moderating influence on the vertical equity index when the number of driver participants at high-income levels remains constant. In general, within a reasonable range, the higher the reference price, the more equitable the parking reservation procedure and the lower the vertical equity index. [ABSTRACT FROM AUTHOR]

Objective: To analyze the equity and efficiency of health resource allocation in township health centers in Sichuan Province, and to provide a scientific basis for promoting the development of township health centers in Sichuan Province, China. Methods: The Lorenz curve, Gini coefficient and health resource density index were used to analyze the equity of health resource allocation in township health centers in Sichuan Province from 2017 to 2021, and data envelopment analysis(DEA) was used to analyze the efficiency of health resource allocation in township health centers in Sichuan Province from 2017 to 2021. Results: The Gini coefficient of health resources of township health centers in Sichuan Province is below 0.2 by population in addition to the number of beds in 2020–2021 and practicing (assistant) physicians in 2021, and the Gini coefficient of health resources of township health centers in Sichuan Province is above 0.6 by geography. The Lorentz curve of health resources of township health centers in Sichuan Province is closer to the equity line by population allocation and further from the equity line by geographical allocation. The average level of township health centers in Sichuan Province is used as the standard to calculate the health resource density standard index(W) of each region, the Ws of Panzhihua, Ganzi, Aba and Liangshan are less than 1, and the Ws of Ziyang, Neijiang, Deyang and Meishan are greater than 1. The overall efficiency of township health centers in Sichuan Province in 2017 and 2021 is 1, and the DEA is relatively effective. The overall efficiency of township health centers in Sichuan Province in 2018 and 2019 is not 1, and the DEA is relatively ineffective. The overall efficiency of all health resources in Mianyang and Ziyang is 1, and the DEA is relatively effective. The overall efficiency of all health resources in Suining, Neijiang, Yibin, Aba and Ganzi is not 1, and the DEA is relatively ineffective. Conclusion: The equity of health resource allocation by population is better than that by geography in township health centers in Sichuan Province. Combining population and geographical factors, the health resource allocation of Panzhihua, Ganzi, Aba and Liangshan is lower than the average level of Sichuan Province. The efficiency of health resource allocation in township health centers in Sichuan Province is low. [ABSTRACT FROM AUTHOR]

We explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve drawn in the map of the tail-integrated cumulative population and wealth fractions. In particular, we rediscover Tsallis' q-entropy formula related to the Pareto distribution. As a novel result, we express the traditional entropy in terms of gintropy and reconstruct further non-additive formulas. A dynamical model calculation of the evolution of Gini index is also presented. [ABSTRACT FROM AUTHOR]

The inequality in leaf and fruit size distribution per plant can be quantified using the Gini index, which is linked to the Lorenz curve depicting the cumulative proportion of leaf (or fruit) size against the cumulative proportion of the number of leaves (or fruits). Prior researches have predominantly employed empirical models—specifically the original performance equation (PE‐1) and its generalized counterpart (GPE‐1)—to fit rotated and right‐shifted Lorenz curves. Notably, another potential performance equation (PE‐2), capable of generating similar curves to PE‐1, has been overlooked and not systematically compared with PE‐1 and GPE‐1. Furthermore, PE‐2 has been extended into a generalized version (GPE‐2). In the present study, we conducted a comparative analysis of these four performance equations, evaluating their applicability in describing Lorenz curves related to plant organ (leaf and fruit) size. Leaf area was measured on 240 culms of dwarf bamboo (Shibataea chinensis Nakai), and fruit volume was measured on 31 field muskmelon plants (Cucumis melo L. var. agrestis Naud.). Across both datasets, the root‐mean‐square errors of all four performance models were consistently smaller than 0.05. Paired t‐tests indicated that GPE‐1 exhibited the lowest root‐mean‐square error and Akaike information criterion value among the four performance equations. However, PE‐2 gave the best close‐to‐linear behavior based on relative curvature measures. This study presents a valuable tool for assessing the inequality of plant organ size distribution. [ABSTRACT FROM AUTHOR]

The problem of examining how well the data fit a supposed distribution is very important, and it must be confirmed prior to any data analysis, because many data analysis methods assume a specific distribution of data. For this purpose, histograms or Q-Q plots are employed for the assessment of data distribution. Additionally, a GoF TstS utilizes distance measurements between the empirical distribution function and the theoretical cumulative distribution function (cdf) to evaluate data distribution. In life-testing or reliability studies, the observed failure time of test units may not be recorded in some situations. The GoF TstSs for completely observed data can no longer be used in progressive type II censored data (PrCsD). In this paper, we suggest a GoF TstSs and new plot method for the GoF test of symmetric and asymmetric location-scale distribution (LoScD) based on PrCsD. The power of the suggested TstSs is estimated through Monte Carlo (MC) simulations, and it is compared with that of the TstSs using the order statistics (OrSt). Furthermore, we analyzed real data examples (symmetric and asymmetric data). [ABSTRACT FROM AUTHOR]

To contribute to the study of networks and graphs. We apply standard mathematical thinking. We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain. As a consequence, the average and median distances in any such network are smaller than or equal to those of a chain. We restricted our investigations to undirected, unweighted networks. We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property. To the best of our knowledge our research contains new network results, especially those related to frequencies of distances. [ABSTRACT FROM AUTHOR]

Background: COVID-19 has reportedly resulted in disparities in the use of telemedicine due to several socioeconomic factors. While telemedicine was developed to overcome geographical distance, under COVID-19 telemedicine conversely might have deepened the urban-rural telemedicine divide. Especially in Japan, the authority has virtually regulated distant telemedicine use, which favored telemedicine providers who are located in close proximity to patients. This study aimed to quantify the urban-rural disparity in access to telemedicine and investigate heterogeneity between devices (phone and video visits). Methods: We used two nationally comprehensive data sources in Japan. One was a municipality-level telemedicine provider database. Municipality-provider-level analysis intended to measure the uneven distribution of telemedicine providers compared to usual health care providers as well as the difference among clinical departments. The second source was prefecture-level telemedicine utilization data. Prefecture-utilization-level analysis aimed to quantify how the use of telemedicine converged in urban areas. We investigated the heterogeneity between types of devices and time periods. To measure inequality, this study used the Lorenz Curve and Gini coefficients. Ethical review was not required. Results: The data included 16,927 providers (14,111 clinics and 2,816 hospitals) and 88,952 first visits throughout Japan. The main findings were the geographically converged distribution of telemedicine providers compared with overall providers who were not limited to telemedicine and, possibly as a result of it, the geographically unequal utilization of telemedicine compared with in-person visits. Furthermore, video visits were more unequally utilized than phone visits, let alone in-person visits. The disparity was not resolved over time, which implied a systematic cause. Conclusion: Using comprehensive nationwide data, this study revealed geographical inequality relating to access to telemedicine under the COVID-19 special deregulation in Japan. While telemedicine initially aimed to provide access to care for people in rural areas, several factors, including the digital divide, COVID-19, and the Japanese policy, paradoxically could have caused this disparity. [ABSTRACT FROM AUTHOR]

The health of city inhabitants is considerably impacted by the urban park green spaces (UPGS). Existing studies lack an assessment of the UPGS equity from different perspectives and are limited to poor accuracy. This study reviews the definition and determination methods of UPGS, as well as UPGS accessibility and spatial equity related studies. Then, a spatial equity evaluation system is established from the dimensions of equity in providing UPGS services and equity in supply and demand matching. This study extrapolates from micro to macro analysis using network big data and census data to pinpoint the population down to the building level in the main urban area of Fuzhou City, China. The network analysis method, improved Gaussian floating catchment area method, Gini coefficient, and Lorenz curve measurement help to evaluate UPGS service euquity, explore the similarities and differences of UPGS fairness under different travel modes. It also helps to understand the service relationship between UPGS service and population demand under objective space, and to pinpoint the weak supply area using the locational entropy method. The results show that: (1) The overall accessibility and per capita accessibility show similar spatial distribution patterns under different travel modes, which are "high around and low in the middle" and "centered on the Minjiang River and dispersed to the north and south, respectively" in study area. (2) The supply of UPGS services in Fuzhou is relatively adequate and at a relatively equity level, while varies in the allocation of UPGS services among sub-districts. The spatial equity of different traveling modes varies widely. (3) The sub-districts on the periphery of the study area should be subject to increased UPGS and improvements to the road network and public infrastructure. Sub-district with high population density and old neighborhoods should implement micro-renewal and build community parks. Our study presents a new idea for spatial equity research. [ABSTRACT FROM AUTHOR]

Diversity, as used in interdisciplinarity studies, has three components: variety, evenness, and dissimilarity. In 2019, Leydesdorff, Wagner, and Bornmann proposed an indicator, denoted as DIV*, that independently operationalized these three components and then combined them. Gini evenness is one factor in this formula. An important point is that Leydesdorff and his colleagues rejected so-called dual concepts, i.e. concepts that mix or are influenced by at least two of the three basic components of diversity. A few years ago Chao and Ricotta took a new look at "evenness" and showed that the Gini evenness measure, as well as the Lorenz curve, are dual concepts as they are influenced by variety. For this reason, I propose to replace the Gini evenness measure in DIV* with an evenness measure, actually an evenness profile, that is not influenced by variety. [ABSTRACT FROM AUTHOR]

Precipitation concentration indices have become a popular tool for analyzing the structure of daily precipitation amounts. Among the existing indices, the concentration index (CI) is widely used. In calculating the CI, an important aspect is adjusting the Lorenz curve based on the observed precipitation data. Usually, the fit has been carried out with equations of the type y = axebx. However, in some research work, it has been observed that sometimes, the fit obtained only partially describes the behavior of the data. Thus, this work evaluated an alternative functional form to fit the Lorenz curve. For this, daily precipitation data from 44 climatological stations in Mexico were used to assess two equations for adjusting the Lorenz curve. Once the fit was made, the goodness of fit was evaluated to determine which of the functional forms best described the behavior of the data. Results showed that the two functional forms produced similar results for low precipitation concentrations. However, when the concentration increased, the alternative functional form generated results following the behavior of the observations. Thus, it is recommended to use the alternative functional form to avoid overestimations of the concentration of daily precipitation in areas where it is known that a high concentration occurs. [ABSTRACT FROM AUTHOR]

Socioeconomic inequalities among foreign-born populations in the United States in minor-emerging gateways are rarely discussed in existing inequality literature. This study helps to fill that gap by examining inequality and spatial integration among immigrant, US–born White, and Black populations in a minor gateway metropolitan area of Greensboro–High Point, NC. The 2020 Census five-year (2016–2020) estimate of American Community Survey (ACS) housing and demographic data, the location quotient (LQ), Lorenz curve, and Gini Index are utilized. The LQ values suggest immigrant groups are more concentrated with Black populations than White populations, but US–born Black and White populations are far more segregated than immigrant groups. Lorenz curve and Gini coefficients confirm that White populations experience the least inequality while the greatest income inequality exists among US–born Black populations, followed by immigrant populations. Further, disparities in income are greater for immigrants living in their underrepresented communities than those who live in overrepresented neighborhoods. The study concludes that immigrant populations living in segregated neighborhoods with a higher proportion of racial and ethnic minorities have lower education and English language competency than those living in neighborhoods with a higher percentage of US–born residents, and hence have lower income inequality among populations. [ABSTRACT FROM AUTHOR]

Equity in the distribution of medical facilities is critical to the effectiveness of healthcare investments and the equality of residents' right to health. In recent years, the Chinese Government has been working to establish a well-organized hierarchical system of medical facilities. However, few studies have focused on the evaluation of multilevel medical facility accessibility and equity, and they are usually based on a single urban road network without considering the distinction between walkways and carriageways. To address these issues, this study analyzed and calculated results on the distribution of multilevel medical facilities in terms of accessibility and equity evaluation based on a Gaussian two-step floating catchment area method, an improved medical facility supply capacity model, and two road networks of walkways and carriageways in the central urban area of Jinan, China. The results showed that the distribution of medical facilities shows the vacuum phenomenon of primary medical facilities and the polarization phenomenon of tertiary medical facilities and that the shortage of accessibility of primary medical facilities is masked when comprehensive accessibility calculations are performed. The results of the Gini coefficient and Lorenz curve showed that the distribution of primary medical facilities is extremely inequitable and that increasing the number of primary medical facilities and their supply capacity remains a priority for China to promote health equity. The results of the aforementioned study suggested strategies for medical facility system improvement and urban road network planning: planning new primary hospitals in densely populated areas, building large general hospitals in the eastern and western edges of the city, building east–west road networks to increase road centerline density, and so on. The improved Gaussian two-step floating catchment area method (Ga2SFCA) helps to construct a spatial accessibility model for multilevel medical facilities, and the adopted methods of accessibility and equity analysis are also useful for siting studies on the layout of other service facilities such as education and elderly care. [ABSTRACT FROM AUTHOR]

Objective: Equity in the delivery of health services, including diagnostic imaging, is crucial to achieving universal health coverage. The Health Transformation Plan (HTP), launched in 2014, represents a major healthcare policy to improve the quality and accessibility of healthcare services. This study aimed to explore the impact of the HTP on equity in the access to medical imaging in Lorestan province, located in west Iran, from 2014 to 2023. Annual growth rates (AGR) of imaging devices were calculated, whilst equity assessment of medical imaging distribution was carried out by means of the Gini coefficient and the Lorenz curve per 100,000 population. The latter was generated using the cumulative distribution of imaging devices, as well as the cumulative population ratio. Results: Between 2014 and 2023, the number of imaging devices has increased threefold. The AGR of installing CT and MRI scanners in Lorestan province increased between 2014 and 2023. The Gini coefficients increased from 0.12 for CT and 0.16 for MRI in 2014 to 0.33 in 2023 for both devices. This indicates a decrease in equity in access to these fundamental health technologies despite the increase in their figures. Policymakers should better allocate medical equipment based on the specific health needs of different regions throughout Iran. [ABSTRACT FROM AUTHOR]

Background: As approximately 3/4 of the population lives in county-level divisions in China, the allocation of health resources at the county level will affect the realization of health equity. This study aims to evaluate the disparity in hospital beds at the county level in China, analyze its causes, and discuss measures to optimize the allocation. Methods: Data were drawn from the Chinese County/City Statistical Yearbook (2001–2020). The health resource density index (HRDI) was applied to mediate between the influence of demographic and geographical factors on the allocation of hospital beds. The trends of HRDI allocation were evaluated through the growth incidence curve and the probability density function. The regional disparity in the HRDI was examined through the Lorenz curve, and Dagum Gini coefficient. The contribution of the Gini coefficient and its change were assessed by using the Dagum Gini decomposition method. Results: From 2000 to 2019, the number of hospital beds per thousand people at the county level in China increased dramatically by 1.49 times. From the aspect of the HRDI, there were large regional disparities at the national level, with a Gini coefficient of 0.367 in 2019 and in the three subregions. In 2019, the Gini coefficient of the HRDI exhibited regional variations, with the highest value observed in the western region, followed by the central region and the eastern region. Decomposition reveals that the contribution of interregional disparity changed from the dominant factor to the least important factor, accounting for 29.79% of the overall disparity and the contribution of trans-variation intensity increased from 29.19% to 39.75%, whereas the intraregional disparity remained stable at approximately 31% and became the second most important factor. Conclusion: The regional disparity in hospital beds allocation at the county level in China was large and has not improved substantially. Trans-variation intensity was the main reason for the overall disparity and changes, and the intraregional disparity was more important than the interregional disparity for the overall disparity. [ABSTRACT FROM AUTHOR]

Out-of-hospital cardiac arrest (OHCA) causes a high mortality rate each year, which is a threat to human well-being and health. An automated external defibrillator (AED) is an effective device for heart attack-related diseases and is a panacea to save OHCA. Most relevant literature focuses on the spatial distribution, accessibility, and configuration optimization of AED devices, which all belong to the characteristics of the spatial distribution of AED devices. Still, there is a lack of discussion on related potential influencing factors. In addition, analysis of AED facilities involving multiple city comparisons is less considered. In this study, data on AED facilities in two major cities in China were obtained through the WeChat applet. Then, the AED equity at the city and block scales and its socioeconomic factors were analyzed using the Gini coefficient, Lorenz curve, and optimal parameters-based geo-graphical detector (OPGD) model. Results show that the number of AEDs in Shenzhen was about eight-times that of in Guangzhou. The distribution of AEDs in Shenzhen was more equitable with a global Gini of 0.347, higher than that in Guangzhou with a global Gini of 0.504. As for the determinants of AED equity, residential density was the most significant determinant in both Guangzhou and Shenzhen from the perspective of individual effects on AED equity. Differently, due to the aging population in Guangzhou, the proportion of the elderly in blocks was influential to local AED equity. The local economic development level was crucial to local AED equity in Shenzhen. The results of the interaction detector model illustrate that relatively equitable AED distributions were found in the high-density residential areas with a balance of employment and housing, high-aging residential areas, and high-mobility residential areas in Guangzhou. The area with a high level of local economic development, dense population, and large mobility was the area with a relatively equitable distribution of AEDs in Shenzhen. The results of this paper are conducive to understanding the equity of AEDs and its socio-economic determinants, providing scientific reference for the optimization and management of AEDs. [ABSTRACT FROM AUTHOR]

A man's baseline prostate-specific antigen level can guide decisions on the repeat screening interval, as demonstrated using 16-yr follow-up data from the ERSPC trial. The European Association of Urology guidelines recommend a risk-based strategy for prostate cancer screening based on the first prostate-specific antigen (PSA) level and age. To analyze the impact of the first PSA level on prostate cancer (PCa) detection and PCa-specific mortality (PCSM) in a population-based screening trial (repeat screening every 2–4 yr). We evaluated 25 589 men aged 55–59 yr, 16 898 men aged 60–64 yr, and 12 936 men aged 65–69 yr who attended at least one screening visit in the European Randomized Study of Screening for Prostate Cancer (ERSPC) trial (screening arm: repeat PSA testing every 2–4 yr and biopsy in cases with elevated PSA; control arm: no active screening offered) during 16-yr follow-up (FU). We assessed the actuarial probability for any PCa and for clinically significant (cs)PCa (Gleason ≥7). Cox proportional-hazards regression was performed to assess whether the association between baseline PSA and PCSM was comparable for all age groups. A Lorenz curve was computed to assess the association between baseline PSA and PCSM for men aged 60–61 yr. The overall actuarial probability at 16 yr ranged from 12% to 16% for any PCa and from 3.7% to 5.7% for csPCa across the age groups. The actuarial probability of csPCa at 16 yr ranged from 1.2–1.5% for men with PSA <1.0 ng/ml to 13.3–13.8% for men with PSA ≥3.0 ng/ml. The association between baseline PSA and PCSM differed marginally among the three age groups. A Lorenz curve for men aged 60–61 yr showed that 92% of lethal PCa cases occurred among those with PSA above the median (1.21 ng/ml). In addition, for men initially screened at age 60–61 yr with baseline PSA <2 ng/ml, further continuation of screening is unlikely to be beneficial after the age of 68–70 yr if PSA is still <2 ng/ml. No case of PCSM emerged in the subsequent 8 yr (up to age 76–78 yr). A limitation is that these results may not be generalizable to an opportunistic screening setting or to contemporary clinical practice. In all age groups, baseline PSA can guide decisions on the repeat screening interval. Baseline PSA of <1.0 ng/ml for men aged 55–69 yr is a strong indicator to delay or stop further screening. In prostate cancer screening, the patient's baseline PSA (prostate-specific antigen) level can be used to guide decisions on when to repeat screening. The PSA test when used according to current knowledge is valuable in helping to reduce the burden of prostate cancer. [ABSTRACT FROM AUTHOR]

This article introduces a new statistical distribution called the power unit Burr-XII distribution, which is an extension of the Burr XII distribution obtained through a power transform. This paper investigates several statistical properties of this new model, including mode, moments, moment generating and characteristic functions, entropy, and Bonferroni and Lorenz curves. In addition, various classical estimators for the parameters of the power unit Burr-XII distribution are evaluated, including maximum likelihood estimates, ordinary least squares estimates, maximum product of interval estimates, Anderson–Darling, right and left tail Anderson–Darling, and Cramer–von Mises estimators. This study provides tables and graphs to illustrate the performance of these methods under different scenarios and sample sizes. The results of the proposed distribution in different fields of application are shown using the mortality rates of COVID-19 patients in Spain and flood data from 20 observations. As a result of both applications, it was observed that the proposed distribution gave better results compared to other well-known distributions, such as the beta distribution, transformed gamma distribution, log-weighted power distribution, transmuted power distribution, Kumaraswamy distribution, Topp–Leone distribution, exponentiated reduce Kies distribution, and exponentiated Topp–Leone distribution. [ABSTRACT FROM AUTHOR]

In this work, a two-parameter continuous distribution, namely the Lehmann type II Teissier distribution is introduced. Some important properties including the Rényi entropy, Bonferroni curves, Lorenz curves and the exact information matrix of the proposed model are derived. Seven different techniques are being used for the estimation of parameters and a simulation is carried out to observe the maximum likelihood estimates. Interval estimates of the parameters are obtained using exact information matrix and bootstrapping techniques. Finally, to show the practical significance, three datasets related to COVID-19 and rainfall are modeled using the proposed model. [ABSTRACT FROM AUTHOR]

This document provides a comprehensive overview of the capacity and distribution of intensive care unit (ICU) beds in China from 2007 to 2021. The study found that the number of ICU beds in China increased significantly during this period, but the proportion of ICU beds in relation to hospital beds remained low at 0.91% in 2021. Furthermore, the number of ICU beds per 100,000 population in China was still insufficient compared to OECD countries. The study also identified regional differences in ICU bed distribution, with some provinces having higher ICU bed availability than others. The authors recommend increasing China's ICU capacity and improving the equitable distribution of ICU beds between regions to meet future demands. [Extracted from the article]

Inequality is present in all human societies, but building a robust understanding of how that inequality developed and persisted for centuries requires historical and archaeological data. Identifying the degree of inequality (or disparity) in ancient communities can be addressed through a variety of methods. One method becoming standard practice in archaeology evaluates inequality through quantitative analysis of robust settlement data. In this Compact Special Section, we assess household size as a potential reflection of wealth inequality among Classic period (a.d. 250–900) Maya settlements. First, we generate house-size data from both pedestrian and remotely sensed LiDAR surveys. Then we use those data to calculate Gini coefficients and Lorenz curves, which provide measures of variation. Gini coefficients range from 0 to 1, where 0 reflects perfect equality and 1 indicates perfect inequality, regardless of the actual values in the distribution. Both area (m2) and volume (m3) provide different, complementary metrics to investigate residential size as a metric for wealth inequality among Classic Maya Lowland settlements. Proposed mechanisms that generate inequality include the intergenerational transmission of wealth and differential access to resources; however, addressing these and other pathways for how inequality develops and persists, and how it was maintained in the past provides insight into similar processes of systemic inequality worldwide. [ABSTRACT FROM AUTHOR]

Being a form of labor investment, house size is frequently analyzed as an index of socioeconomic inequality. However, datasets that lack wide-ranging residential stratigraphic information are not reliable sources of labor investment estimates. This is the case for Late Classic domestic architecture data from three polities in the Rosario Valley (modern-day Chiapas) on the southwest Maya frontier: Rosario, Ojo de Agua, and Los Encuentros. Although the sample's house size inequality generally cannot index period-specific labor investment, it may signify prestige differentiation. For each polity we generated Lorenz curves and calculated Gini coefficients for five variables representing house size (area and volume). Results resemble inequality data from lowland Classic Maya centers. We also demonstrate that the smallest, shortest-lived polity had more equal house size values, likely due to the modesty of its apical elite architecture. In contrast, the two larger, older polities were more unequal because they had substantial palaces. [ABSTRACT FROM AUTHOR]

During the Late Classic period (a.d. 550–900), ancient Maya settlement spread throughout western Belize, including the Vaca Plateau, a rugged karstic region with high densities of ritually utilized cave systems. Within the past decade, archaeologists have increasingly drawn on LiDAR technology to document the extent of such settlement at local and regional scales. Combined with traditional pedestrian survey, we have begun to amass substantial data on variation within household groups, disparities which may indicate inequality within these communities. Here, we use settlement data generated from the Las Cuevas region to quantify residential variation through Gini coefficients and Lorenz curves. Special attention is given to areal and volumetric deviation of identified households within three samples: (1) the complete 95.25 km2 study area; (2) a 12.25 km2 zone of higher population between the primary centers of Las Cuevas and Monkey Tail; and (3) households situated within 500 m of ritually utilized caves within the study area. Results indicate some degree of variation within household area and volume for all samples, suggestive of unequal access to labor within the region. This research adds to the growing database of Gini-based analyses to improve our understanding of wealth differentials within pre-modern populations throughout the Lowlands. [ABSTRACT FROM AUTHOR]

Gini coefficients for residential groups at Coba for roofed surface area, volume of architecture, and houselot space range from 0.423 to 0.551, fitting well within the range of many ancient and modern state-level cities and societies and other Mesoamerican centers. These values are also similar to other large, Classic period, Northern Lowland cities, such as Dzibilchaltun and Chunchucmil. These data do not support the idea that autocratic regimes exhibit greater wealth inequality. We also failed to find a pattern in which inequality grew over the course of the Classic period. The Lorenz curves for Coba and other sites do not indicate any breaks that would allow households to be sorted into wealth classes. Thus, wealth differences were fluid, continuous, and out in the open, giving these settlements the dynamism and attractiveness that helped them grow into some of the largest and most remarkable ancient Maya cities. [ABSTRACT FROM AUTHOR]

The Lorenz curve is a fundamental tool for analyzing income and wealth distribution and inequality. Indeed, the Lorenz curve and its derivative, the so‐called share density, provide valuable information regarding inequality. There is a widely recognized connection between the Lorenz curve and elements from information theory field. Starting from this evidence, the aim of this work is to compare the income inequality of different subgroups, by using a proper dissimilarity measure, borrowed from information theory, between parametric share densities. This measure is then considered for clustering purposes. To this end, a dynamic clustering algorithm is considered to group unconventional data, such as density functions. Finally, an application, regarding data from Survey on Households Income and Wealth (SHIW) by Bank of Italy, is shown. [ABSTRACT FROM AUTHOR]

The paper reviews the " κ -generalized distribution", a statistical model for the analysis of income data. Basic analytical properties, interrelationships with other distributions, and standard measures of inequality such as the Gini index and the Lorenz curve are covered. An extension of the basic model that best fits wealth data is also discussed. The new and old empirical evidence presented in the article shows that the κ -generalized model of income/wealth is often in very good agreement with the observed data. [ABSTRACT FROM AUTHOR]

Background: General practitioners (GP) are the gatekeepers of residents' health, 2021 is the 10th year of the establishment of the GP system in China. This study aims to assess the equity and trends of GP allocation in China from 2012 to 2021, summarize the efforts and progress of GPs in China during the decade, predict the development trend of GPs in mainland China in the next 5 years to provide a reference for regional health planning and rational allocation of GPs in China. Methods: Data from 2012 to 2021 on GPs in 22 provinces, 5 autonomous regions, and 4 municipalities directly under the central government in mainland China (excluding Hong Kong, Macao, and Taiwan) are collected by us. Gini coefficient, Lorenz curve and health resource agglomeration degree (HRAD) were used to analyze the equity of the allocation of GPs in China from different dimensions, a Grey prediction model was used to forecast the number of GPs in 2022–2026. Results: The number of GPs in mainland China increased from 109 794 to 434 868 from 2012 to 2021, with 3.08 GPs per 10 000 people in 2021. The Gini coefficient of GPs allocation by population in China decreased from 0.312 to 0.147 from 2012 to 2021, while the Gini coefficient of geographic dimension remained between 0.700 and 0.750. Compared with the degree of curvature of the Lorenz curve in the geographic dimension, the degree of curvature of the population and economic dimension were smaller. In 2021, the HRAD in the Eastern region was 4.618, the Central region was 1.493, with different degrees of imbalance among regions, the HRAD/PAD (population agglomeration degree) in the Eastern, Central and Western regions were 1.196, 0.880 and 0.821, respectively. GPs in the Eastern region is still concentrated, while the Central and Western regions were at a similar level, GPs were more scarce. The GM (1,1) model predicts that the number of GPs in mainland China will reach about 720 000 in 2026, the number of GPs per 10 000 people will reach 4.9. Conclusion: After a decade of development, the number of GPs in China has increased significantly. It has reached the goal of the GP system when it was first established. However, the equity of the geographical dimension, both in terms of Gini coefficient and HRAD, has great differences between different regions. The average Gini coefficient at the geographic dimension is 0.723. The average HRAD index was 4.969 in the East and 0.293 in the West. The Western region has the problem of insufficient GP allocation in both population and geographical dimension. In the future, the number of GPs in China will continue to grow rapidly with the support of policies. The "2030" goal, proposed in 2018, is expected to be achieved by 2026. Due to certain factors (such as COVID-19), the actual situation may be different from the predicted results. [ABSTRACT FROM AUTHOR]

Education is one of the most significant investments a nation can make in its citizens that can address poverty and inequality in the nearest future. This study sought to assess the spatial pattern of public primary schools in Moro Local Government Area (LGA) of Kwara State, Nigeria. The purpose of the study was to look at the geographic distribution and the level of inequality of the public primary schools in the study area. The number, names and addresses of public primary schools were obtained from the unit of the planning, research and statistics department of Moro Local Government Education Authority (MGLEA) while the data on the geographic location of the public primary schools were gotten via GPS device (Mreno 120, Garmin). Descriptive statistics such as frequency, percentages and Lorenz curve were used to assess the distribution of public primary schools in the study area. These data were also analyzed using Nearest Neighbour Analysis (NNA) to derive the spatial pattern of public primary schools in the area. Findings revealed that there are one hundred and fifty six (156) public primary schools in Moro LGA. Findings further revealed that Malete had the highest percentage of public primary schools with 10.3%, followed by Megida with 9.6% while Ajanaku and Pakunma had the least public primary schools, with 1.9% and 2.6%, respectively. The NNA result of the spatial pattern of public primary schools produced a clustered pattern at 0.01% significance level with the Nearest Neighbour Ratio (NNR) of 0.86 and a Z-Score of -3.39. The paper consequently recommends that Moro LGC should liaise with the Kwara state government and other relevant stakeholders in order to ensure that the allocation of primary schools is distributed equitably throughout the LGA for easy accessibility. [ABSTRACT FROM AUTHOR]

Background. The COVID-19 pandemic has spread rapidly to all countries with significant health, socioeconomic, and political consequences. Several safe and effective vaccines have been developed. However, it is not certain that all African countries have successfully vaccinated their populations. Objective. To study the distribution and determinants of COVID-19 vaccination in Africa from March 2021 to June 2022. Methods. Using reliable open-access data, we used the proportion of fully vaccinated people with a complete schedule as a reference variable. To analyze the level of inequality in COVID-19 vaccination, we computed common inequality indicators including two percentile ratios, the Generalized Entropy index, the Gini coefficient, and the Atkinson index. We also estimated the Lorenz curve. To identify drivers of COVID-19 vaccination, we estimated univariate and multivariate regression models as a function of COVID-19-related variables, demographic, epidemiologic, socio-economic, and health system-related variables. To overcome a potential endogeneity bias, we checked our results using simultaneous equation models. Results. 53 African countries with available data were included in the study. The proportion of fully vaccinated people increased during the study period. However, this increase remained unequal across African countries. Based on the inequality indicators and the Lorenz curve, inequalities in COVID-19 vaccination across African countries were high, although they have decreased in recent months. Total COVID-19 cases and human development index were identified as significant determinant factors that were independently associated with COVID-19 vaccination. Conclusions. Inequality in COVID-19 vaccination in Africa was high. Promoting adequate information to the general population and providing financial and logistical support to low-income countries can help expand COVID-19 vaccination in Africa. [ABSTRACT FROM AUTHOR]

Despite a significant drop in maternal mortality in Bangladesh, unsafe abortion remains a critical maternal health issue that could be reduced by promoting menstrual regulation (MR). This study aimed to investigate the prevalence and determinants of MR use among ever-married women as well as to identify the socioeconomic inequalities in MR use in Bangladesh. The latest Bangladesh Demographic and Health Survey (BDHS) 2017-18 data were used in this study. We used a sub-sample of 12,586 ever-married women aged 15 to 49 years for this study. To identify the determinants of MR, multilevel (mixed-effect) binary logistic regression analysis was used while accounting for potential between-clusters variations. The weighted prevalence of MR was 7.64% (95% CI: 7.19 - 8.12). Women of aged 20-29 years (AOR: 2.50, 95% CI: 1.46, 4.30) and ≥ 30 years (AOR: 4.17, 95% CI: 2.39, 7.26), from urban areas (AOR: 1.24, 95% CI: 1.04, 1.47), having one or two children (AOR: 1.96, 95% CI: 1.25, 3.09) and ≥ 3 children (AOR: 2.26, 95% CI: 1.40, 3.65), who used traditional contraceptive method (AOR: 1.39, 95% CI: 1.12, 1.73), and from Barishal division (AOR: 1.44, 95% CI: 1.08, 1.93) were more likely to have MR. Women were less likely to have MR if they were from Chittagong (AOR: 0.62, 95% CI: 0.46, 0.84) and Mymensingh (AOR: 0.51, 95% CI: 0.36, 0.73) divisions. MR use was found to be higher among higher socioeconomic status (SES) groups as the concentration index (CIX) value was positive and the Lorenz curve lay below the line of equality (CIX: 0.095, p<0.001). Health policy and intervention design should prioritize minimizing socioeconomic inequities concerning MR services. [ABSTRACT FROM AUTHOR]

Given that an excellent performance of any parametric functional form for the Lorenz curve that is based on a single country case study and a limited range of distribution must be treated with great caution, this study investigates the performance of a single-parameter functional form proposed by Paul and Shankar (2020) who use income data of Australia to show that their functional form is superior to the other existing widely used functional forms considered in their study. By using both mathematical proof and empirical data of 40 countries around the world, this study demonstrates that Paul and Shankar (2020)'s functional form not only fails to fit the actual observations well but also is generally outperformed by the other popular functional forms considered in their study. Moreover, to overcome the limitation of the performance of a single-parameter functional form on the criterion of the estimated Gini index, this study employs a functional form that has more than one parameter in order to show that, by and large, it performs better than all popular single-parameter functional forms considered in Paul and Shankar (2020)'s study. Thus, before applying any functional form to estimate the Lorenz curve, policymakers should check if it could describe the shape of income distributions of different countries through the changes in parameter values and yield the values of the estimated Gini index that are close to their observed data. Using a functional form that does not fit the actual observations could adversely affect inequality measures and income distribution policies. [ABSTRACT FROM AUTHOR]

Background: Understanding geospatial impacts of multi-sourced influencing factors on the epidemic of hand-foot-and-mouth disease (HFMD) is of great significance for formulating disease control policies tailored to regional-specific needs, yet the knowledge is very limited. We aim to identify and further quantify the spatiotemporal heterogeneous effects of environmental and socioeconomic factors on HFMD dynamics. Methods: We collected monthly province-level HFMD incidence and related environmental and socioeconomic data in China during 2009–2018. Hierarchical Bayesian models were constructed to investigate the spatiotemporal relationships between regional HFMD and various covariates: linear and nonlinear effects for environmental covariates, and linear effects for socioeconomic covariates. Results: The spatiotemporal distribution of HFMD cases was highly heterogeneous, indicated by the Lorenz curves and the corresponding Gini indices. The peak time (R2 = 0.65, P = 0.009), annual amplitude (R2 = 0.94, P<0.001), and semi-annual periodicity contribution (R2 = 0.88, P<0.001) displayed marked latitudinal gradients in Central China region. The most likely cluster areas for HFMD were located in south China (Guangdong, Guangxi, Hunan, Hainan) from April 2013 to October 2017. The Bayesian models achieved the best predictive performance (R2 = 0.87, P<0.001). We found significant nonlinear associations between monthly average temperature, relative humidity, normalized difference vegetation index and HFMD transmission. Besides, population density (RR = 1.261; 95%CI, 1.169–1.353), birth rate (RR = 1.058; 95%CI, 1.025–1.090), real GDP per capita (RR = 1.163; 95%CI, 1.033–1.310) and school vacation (RR = 0.507; 95%CI, 0.459–0.559) were identified to have positive or negative effects on HFMD respectively. Our model could successfully predict months with HFMD outbreaks versus non-outbreaks in provinces of China from Jan 2009 to Dec 2018. Conclusions: Our study highlights the importance of refined spatial and temporal data, as well as environmental and socioeconomic information, on HFMD transmission dynamics. The spatiotemporal analysis framework may provide insights into adjusting regional interventions to local conditions and temporal variations in broader natural and social sciences. Author summary: Hand-foot-and-mouth disease (HFMD) is one of the most common pediatric infectious diseases worldwide and it has affected up to two million children annually in China since 2008. This study used Bayesian spatiotemporal modeling to analyze provincial-level HFMD cases, environmental and socioeconomic data during 2009–2018. We found that both environmental (temperature, relative humidity and normalized difference vegetation index) and socioeconomic covariates (population density, birth rate, real GDP per capita and school vacation) are associated with HFMD occurrence under spatiotemporal scales. This model may help to (1) identify outbreaks of HFMD, including their timing, location and severity; (2) understand the transmission dynamics by mapping the spread of HFMD over time and space; (3) indicate areas of higher risk or the emergence of new outbreaks by detecting clusters of HFMD cases in specific geographic locations. Overall, this study provides valuable information for public health decision-makers and researchers, allowing them to better understand the spread of the disease and target their efforts more efficiently to control its transmission and prevent outbreaks. [ABSTRACT FROM AUTHOR]

Selecting the k best features is a common task in machine learning. Typically, a few features have high importance, but many have low importance (right-skewed distribution). This report proposes a numerically precise method to address this skewed feature importance distribution in order to reduce a feature set to the informative minimum of items. Computed ABC analysis (cABC) is an item categorization method that aims to identify the most important items by partitioning a set of non-negative numerical items into subsets "A", "B", and "C" such that subset "A" contains the "few important" items based on specific properties of ABC curves defined by their relationship to Lorenz curves. In its recursive form, the cABC analysis can be applied again to subset "A". A generic image dataset and three biomedical datasets (lipidomics and two genomics datasets) with a large number of variables were used to perform the experiments. The experimental results show that the recursive cABC analysis limits the dimensions of the data projection to a minimum where the relevant information is still preserved and directs the feature selection in machine learning to the most important class-relevant information, including filtering feature sets for nonsense variables. Feature sets were reduced to 10% or less of the original variables and still provided accurate classification in data not used for feature selection. cABC analysis, in its recursive variant, provides a computationally precise means of reducing information to a minimum. The minimum is the result of a computation of the number of k most relevant items, rather than a decision to select the k best items from a list. In addition, there are precise criteria for stopping the reduction process. The reduction to the most important features can improve the human understanding of the properties of the data set. The cABC method is implemented in the Python package "cABCanalysis" available at https://pypi.org/project/cABCanalysis/. [ABSTRACT FROM AUTHOR]

Much effort has recently been expended in developing efficient models that can depict the true picture for COVID-19 mortality data and help scientists choose the best-fit models. As a result, this research intends to provide a new G family for both theoretical and practical scientists that solves the concerns typically encountered in both normal and non-normal random events. The new-G distribution family is able to generate efficient continuous univariate and skewed models that may outperform the baseline model. The analytic properties of the new-G family and its sub-model are investigated and described, as well as a theoretical framework. The parameters were estimated using a classical approach along with an extensive simulation study to assess the behaviour of the parameters. The efficiency of the new-G family is discussed using one of its sub-models on COVID-19 mortality data sets. [ABSTRACT FROM AUTHOR]

In this paper, a new lifetime distribution called compounded geometric-mixture exponential distribution is proposed by compounding the mixture exponential and geometric distributions. Some properties of the new distribution such as survival function, hazard function, moments, Lorenz and Bonferroni curves, etc. are obtained. The estimations of four parameters of the new model are studied by several methods. A Monte Carlo simulation study is performed to understand the behavior of estimators. Two real data applications are also provided. [ABSTRACT FROM AUTHOR]

The present study deals with a new version of power quasi Lindley distribution known as weighted power quasi Lindley distribution. Its different mathematical and statistical properties like moments, order statistics, reliability analysis, Renyi entropy, bonferroni and Lorenz curves have been presented. The parameters of proposed new distribution are estimated by employing the method of maximum likelihood estimation. Finally, a new distribution has been illustrated with three real lifetime data sets from medical sciences to examine its significance and supremacy. [ABSTRACT FROM AUTHOR]

Given that the existing parametric functional forms for the Lorenz curve do not fit all possible size distributions, a universal parametric functional form is introduced. By using the empirical data from different scientific disciplines and also the hypothetical data, this study shows that, the proposed model fits not only the data whose actual Lorenz plots have a typical convex segment but also the data whose actual Lorenz plots have both horizontal and convex segments practically well. It also perfectly fits the data whose observation is larger in size while the rest of observations are smaller and equal in size as characterized by two positive-slope linear segments. In addition, the proposed model has a closed-form expression for the Gini index, making it computationally convenient to calculate. Considering that the Lorenz curve and the Gini index are widely used in various disciplines of sciences, the proposed model and the closed-form expression for the Gini index could be used as alternative tools to analyze size distributions of non-negative quantities and examine their inequalities or unevennesses. [ABSTRACT FROM AUTHOR]

This article combines demographic and spatial data to investigate and analyse spatial variations in population distribution in Al-Madinah Al-Munawarah in the Kingdom of Saudi Arabia. Drawing on multiple data sources, it applies a straightforward rationalisation-based methodology based on combining demographic indicators with spatial data using geographic information systems and remote sensing. The findings show that Al-Madinah's population was estimated at 1,500,000 people in 2020; the Lorenz curve and the Gini ratio reveal that the population is unevenly distributed geographically since 95% of the population lives in 18% of the city's total area. The central area is densely populated: about half of the population lives within a 5-kilometre radius. Location quotient values reflect variations between concentrations of Saudis and non-Saudis. Due to the expansion of the city's builtup area, net population density fell from 46 to 32 p/ha between 2004 and 2020; Saudis are more mobile than non-Saudis as their mean centres recently shifted 1,337 and 665 meters south, respectively. The study concluded that Al-Madinah's residents, especially Saudis, are gradually moving from the central business district to the periphery. [ABSTRACT FROM AUTHOR]

In this study, we propose a generalized Marshall-Olkin exponentiated exponential distribution as a submodel of the family of generalized Marshall-Olkin distribution. Some statistical properties of the proposed distribution are examined such as moments, the moment-generating function, incomplete moment, and Lorenz and Bonferroni curves. We give five estimators for the unknown parameters of the proposed distribution based on maximum likelihood, least squares, weighted least squares, and the Anderson-Darling and Cramer-von Mises methods of estimation. To investigate the finite sample properties of the estimators, a comprehensive Monte Carlo simulation study is conducted for the models with three sets of randomly selected parameter values. Finally, four different real data applications are presented to demonstrate the usefulness of the proposed distribution in real life. [ABSTRACT FROM AUTHOR]

Background: Equitable geographic distribution of doctors is crucial for the provision of an accessible and efficient health service system. This study aimed to assess the effects of doctor allocation by the Thai Ministry of Public Health (MoPH) in relation to equity distribution. Methods: This descriptive study compared secondary data on the number of doctors, gross provincial products (GPP), and populations of 76 Thai provinces for the years 2017 and 2021. The ratio of doctors to 1000 population was used to measure the spatial distribution of doctors by province. Lorenz curves and the Gini coefficient were used to determine the equity of doctor distribution. Results: The results showed that the Gini coefficient decreased from 0.191 in 2017 to 0.03 in 2021 indicating that the equitable distribution of doctors improved after the MoPH commenced allocating newly graduated doctors according to health utilization in 2017. Compared to 2017, the percentage changes in the number of doctors were higher in provinces with lower doctor densities and in provinces with higher GPPs. Conclusion: The equitable distribution of doctors in Thailand was affected by two main causes: the allocation of newly graduated doctors by the MoPH and the turnover rate of existing doctors. [ABSTRACT FROM AUTHOR]

The recent advent of powerful generative models has triggered the renewed development of quantitative measures to assess the proximity of two probability distributions. As the scalar Frechet Inception Distance remains popular, several methods have explored computing entire curves, which reveal the trade-off between the fidelity and variability of the first distribution with respect to the second one. Several of such variants have been proposed independently and while intuitively similar, their relationship has not yet been made explicit. In an effort to make the emerging picture of generative evaluation more clear, we propose a unification of four curves known respectively as: the Precision-Recall (PR) curve, the Lorenz curve, the Receiver Operating Characteristic (ROC) curve and a special case of Rényi divergence frontiers. In addition, we discuss possible links between PR / Lorenz curves with the derivation of domain adaptation bounds. [ABSTRACT FROM AUTHOR]

Introduction: The link between air pollution-attributed cardiovascular disease (APACVD) burden and its contributing factors can aid in detecting vulnerabilities and providing forewarnings for India.Methods: We examined the association between the status and trends of the APACVD burden obtained from the Global Burden of Diseases and Injuries study with the two development metrics in India; the human development index (HDI) and indirect indices of economic development, namely annual new motor vehicle registration and the number of functional factories for 10 years from 2009 to 2019. Lorenz curves and concentration index were used to estimate the inequalities in the state-APACVD burden and the burden per 100,000 population.Results: At the state level, APACVD burden was inversely related to the HDI value in India for the years 2009 (r=-0.48), 2014 (r=-0.47), and 2019 (r=-0.37), and the association was statistically significant (p<0.05). The correlation between state-level APACVD burden with the annual new motor vehicle registration and the number of functional factories in India for these years was also positive and significant (p<0.05). The APACVD was 53% unequally distributed across the states, with a concentration index of 0.53 in 2009.Discussion: We observed that at the state level, the APACVD burden was inversely related to HDI. But the APACVD burden increased with the country's economic development. Also, the excess APACVD burden appears to be attributable to the economically developed states.Conclusion: At the state level, APACVD burden decreased as HDI rose over time, indicating that the burden increased with the country's economic development. It is noticeable that the economically developed states may be contributing a higher share of the APACVD burden in India. [ABSTRACT FROM AUTHOR]

Introduction: this study aims to examine health inequalities among Korean workers by sex, age, education, monthly income, occupation, and employment type and identify groups of workers who may be neglected in the process of resolving health inequalities. Methods: we used data from the Fourth Korean Working Condition Survey conducted by the Korea Occupational Safety and Health Research Institute and compared the number of health symptoms among various groups using the t-test and one-way analysis of variance to determine their health status. We also calculated the Gini index of the number of health symptoms of each group and plotted the Lorenz curve to illustrate health inequalities. Results: we found that the number of health symptoms was higher in groups with lower socioeconomic status (e.g., female, blue-collar workers, older, low education, low monthly income, and self-employed workers). However, the Gini index and Lorenz curve with respect to socioeconomic status indicated that health inequalities were higher among whitecollar and permanent workers vis-à-vis blue-collar and self-employed workers, respectively. Further, it was found that health inequalities were higher among males than females with respect to the same occupational groups and employment types. Conclusion: general health policies are often targeted at the socially and economically vulnerable group, but according to the results of this study, it can be considered that there may be subjects who are vulnerable to health problems even in groups that are not socioeconomically vulnerable. [ABSTRACT FROM AUTHOR]

Weighted distributions play an important role when observations from a sample are recorded with unequal probabilities. They are useful for the efficient modeling of statistical data when the original distributions are not appropriate. In this paper, a new weighted distribution is proposed. Various statistical properties of the proposed distribution such as survival function, hazard rate function, mean residual life function, moments, moment generating function, Bonferroni curve, Lorenz curve, and order statistic are presented. The Bayesian estimator of the distribution parameter is derived. The behavior of the Bayesian estimator is assessed by a simulation study. Furthermore, a regression model is developed based on the proposed distribution. Some real data applications are analyzed to show the potentiality of the proposed models. [ABSTRACT FROM AUTHOR]

As the aging of China's population continues to deepen, a number of elderly care facilities relying on community platforms to provide home care services have been established in urban communities, effectively alleviating the problem of difficult community elderly care, while a spatial mismatch between the facilities and the elderly population has also emerged. To solve this problem, this paper analyzes the equity in walking access to community home care facilities for elderly people with different mobility abilities in Lianhu District of Xi'an City, taking the resources of community home care facilities as the research object. Firstly, the coverage rate of the facilities was calculated based on the 15-minute walking range of the elderly with different mobility, and the accessibility of the facilities was measured using the Kernel Density-type two-step moving search method. Then, Gini coefficient, Lorenz curve and location entropy were used to analyze the spatial matching pattern of facilities and elderly population. The results show that there is a serious spatial mismatch between the resources of community home care facilities and the elderly population with mobility restriction. In addition, the available facility area per capita is low for more than 80% of the elderly with mobility restriction, and the road network density has a significant impact on the access of the elderly with mobility restriction to the community home care facility resources. These research results indicate that the spatial layout and configuration of community home care facilities are unfair to the elderly with poor mobility, and that these elderly care facility configurations do not favor the disadvantaged groups. [ABSTRACT FROM AUTHOR]