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In this paper, a simple survey technique is applied to estimate the population proportion π of a sensitive trait, in addition to T, the probability that a respondent truthfully states that he or she bears a sensitive character when questioned directly and examined its properties. It has been found that the suggested model is efficient. Numerical illustrations are presented to support the theoretical results.

BACKGROUND: The quality of care is greatly compromised specially in resource limited settings that influence the uptake and continuation of use of family planning services. However, there is paucity of studies in Jimma Town public hospitals. Thus this study aimed to assess the quality of family planning services and associated factors in Jimma Town public hospitals, Southwest Ethiopia.METHODS: A facility-based cross-sectional study design using both qualitative and quantitative methods was employed from March 25 to April 25, 2018. A total of 278 female family planning users (15-49 years old) in Jimma Town public hospitals were included in the study.The sample was calculated using single population proportion formula and consecutive sampling methods was used. Descriptive statistics and multiple logistic regressions were used for analysisis.RESULTS: The mean waiting time of the client before getting service and mean consultation duration were23.5 and 12.5 minutes respectively participant who were unable to read and write were 64% less likely to be satisfied than those who were completed primary and secondary or preparatory schooling (AOR=0.363:CI:0.160,0.822),and clients who were waited for < 30 minutes at waiting area were 2.7 times more likely to be satisfied than those who waited ≥ 30 minutes (AOR=2.769:CI:1.300,5.898).CONCLUSIONS: In this study, the satisfaction of clients in family planning service was low. Waiting time and received information on what to do in cases of problems and educational level of clients were significant predictors of client satisfaction.

In this study, we propose optional randomized response technique (RRT) models in binary response situation. Gupta, Gupta, and Singh (2002) introduced the basic premise of optional RRT model, that a...

Objective The main objective of this study was to assess the prevalence of pressure ulcer and its risk factors among adult hospitalized patients at Dessie Referral Hospital, Northeast Ethiopia, 2016 G.C Result A cross-sectional institutional based study with a single population proportion formula was used to determine the sample size. The total sample size of 355 patients was distributed proportionally to the respected wards. Every other patient was selected by systematic random sampling technique from each ward with a response rate of 100% A total of 53 patients with pressure ulcer were detected giving the prevalence rate of 14.9%. The lack of regular positioning and activity, friction/shear, and prolonged hospitalization were risk factors for pressure ulcer.

The survey related to stigmatized characteristics leads to the non-response problem if it is conducted according to classical (direct) methods, especially, developed for non-sensitive issues; therefore, it needs to be applied appropriate survey methodology to get a reliable response from respondents in incriminating issues. Randomized response model is one of the most recent methods which is attracting the attention of survey practitioners to deal with the problems of non-response because it protects the privacy of individuals in order to acquire the truthful response. The present work proposes a new two-stage randomized response model to get rid of misleading response or non-response due to the stigmatized nature of attribute under the study. The proposed randomized response model results in the unbiased estimator of population proportion possessing the sensitive attribute. The properties of the resultant estimator have been studied and empirical comparisons are performed to show its dominance ov...

Purpose Recent research has confirmed an underlying economic logic that connects each of the three vertices of the “fraud triangle” – a fundamental criminological model of factors driving occupational fraud. It is postulated that in the presence of economic motivation and opportunity (the first two vertices of the fraud triangle), the likelihood of an occupational fraud happening in an organization increases substantially if the overall organization culture is perceived as being slack toward fraud as it helps potential fraudsters in rationalizing their actions (rationalization being the third vertex of the fraud triangle). This paper aims to offer a viable approach for collecting and processing of data to identify and operationalize the key factors underlying employee perception of organization culture toward occupational frauds. Design/methodology/approach This paper reports and analyses the results of a pilot study conducted using a convenience sampling approach to identify and operationalize the key factors underlying employee perception of organization culture with respect to occupational frauds. Given a very small sample size, a numerical testing technique based on the binomial distribution has been applied to test for significance of the proportion of respondents who agree that a lenient organizational culture toward fraud can create a rationalization for fraud. Findings The null hypothesis assumed no difference in the population proportions between those who agree and those who disagree with the view that a lenient organizational culture toward fraud can create a rationalization for fraud. Based on the results of the numerical test, the null hypothesis is rejected in favor of the alternative that the population proportion of those who agree with the stated view in fact exceeded the proportion of those who disagreed. Research limitations/implications The obvious limitation is the very small size of the sample obtained because of an extremely low rate of response to the survey questionnaires. However, while of course a much bigger data set needs to be collected to develop a generalizable prediction model, the small sample was enough for the purpose of a pilot study. Practical implications This paper makes two distinct practical contributions. First, it posits a viable empirical research plan for identifying, collecting and processing the right data to identify and operationalize the key underlying factors that capture an employee’s perception of organizational culture toward fraud as a basis for rationalizing an act of fraud. Second, it demonstrates via a small-scale pilot study that a more broad-based survey can indeed prove to be extremely useful in collating the sort of data that is needed to develop a computational model for predicting the likelihood of occupational fraud in any organization. Originality/value This paper provides a viable framework which empirical researchers can follow to test some of the latest advances in the “fraud triangle” theory. It outlines a systematic and focused data collection method via a well-designed questionnaire that is effectively applicable to future surveys that are scaled up to collect data at a nationwide level.

Sihm et al. (2016) proposed an unrelated question binary optional randomized response technique (RRT) model for estimating the proportion of population that possess a sensitive characteristic and the sensitivity level of the question. In our work, decision theoretic approach has been followed to obtain Bayes estimates of the two parameters along with their corresponding minimal Bayes posterior expected losses (BPEL) using beta prior and squared error loss function (SELF). Relative losses are also examined to compare the performances of the Bayes estimates with those of the classical estimates obtained by Sihm et al. (2016). The results obtained are illustrated with the help of real survey data using non informative prior.

This paper proposes an efficient stratified randomized response model based on Chang et al.'s (2004) model. We have obtained the variance of the proposed estimator of πs, the proportion of the resp...

In this article, we consider a dichotomous population characterized by the parameter p defined as the proportion of individuals in the population possessing certain characteristic. The unknown proportion p is our parameter of interest in the present work. Under the assumption that p is a random quantity we derive a Bayesian Crammer–Rao (BCR) bound in connection with the estimation of p. The proposed procedure is based on a ranked set sample (RSS) observed on the variable of interest which is binary in nature. This RSS-based approach is compared with its corresponding SRS (simple random sample) counterpart in the cases of both perfect and imperfect rankings. The proposed procedure is applied for estimating the proportion of children aged months (to the mothers aged 15–49 years of rural India) who are not immunized with the vaccine against measles using National Family Health Survey-3 (2005–2006) data of India.

In this paper we have suggested a generalized version of the Gjestvang and Singh (2006) model and have studied its properties. We have shown that the randomized response models due to Warner (1965), Mangat and Singh (1990), Mangat (1994) and Gjestvang and Singh (2006) are members of the proposed RR model. The conditions are obtained in which the suggested RR model is more efficient than the Warner (1965) model, Mangat and Singh (1990) model and Mangat (1994) model and Gjestvang and Singh (2006) model. A numerical illustration is given in support of the present study.

Tea expansion, a typical process of regional land use and cover change (LUCC), has raised great concerns on regional sustainability. In this regard, exploring the determinants of tea expansion should provide critical implications for land use policy. It has been widely recognized that LUCC interacts nonlinearly with a set of determinants and their feedbacks should be rather complex. Policy makers are now facing the challenge to identify, apportion, and compare the determinants of regional tea expansion for designing more targeted political intervenes. Our paper utilizes a robust tool, the random forest (RF) regression in particular, to explore the determinants of tea expansion across two periods (1985–2007 and 2007–2016) in Anji County, a typical region of tea production in subtropical China. More specifically, tea is extracted from Landsat imageries and total tea cultivated area acts as the dependent variable. Exploratory variables include 38 potential determinants and these determinants are divided into two categories (biophysical and socioeconomic) at two levels (pixel and village). We obtain some similar findings, though the relative importance of determinants varies with the two periods. In general, biophysical determinants (e.g., topography, soil type, land use in the neighborhood) present greater relative importance than the socioeconomic determinants in both periods. In period 1985–2007, biophysical determinants at pixel level are more essential in governing tea expansion. In period 2007–2016, the relative importance of pixel level biophysical determinants is comparable with that of the village level determinants. Comparisons of the two periods indicate that relative importance of soil type and socioeconomic proximity becomes greater in period 2007–2016, while that of the total employees and non-agricultural population proportion becomes lower. Partial dependency plots are further drawn to visualize the marginal effect of each determinant. We finally propose three options for land use policy towards sustainability. Our study demonstrates that the RF regression is efficient for policy makers to understand the determinants of tea expansion with a nonlinear and complex nature.

We propose a new estimator for the population proportion using a concomitant-based ranked set sampling (RSS) scheme. Simulation results show that the new estimator beats the standard estimator in the RSS as long as the ranking quality is fairly good.

Purpose: To estimate the number of adult transgender women (TGW) in San Francisco and to provide an example of how estimation can be conducted.Methods: Using nine different services accessed by the TGW population, the service multiplier, integrated into a respondent-driven sampling (RDS) survey of TGW, was used to calculate nine estimates of the TGW population in San Francisco. Both the successive sampling method, also integrated into the RDS survey of TGW, and a population proportion from the literature each calculated an additional estimate of the TGW population. The median of all 11 estimates was calculated to present a single estimate of the TGW population in San Francisco.Results: The median of estimates was 978 TGW in San Francisco (plausibility bounds 635 – 1,400). This estimate is consistent with known cases of HIV among TGW and surveys on the prevalence of infection in the TGW population.Conclusion: Using multiple methods, we estimate the TGW population size to be 0.13% of the San Francis...

This paper is concerned with the problem of estimating a population proportion p in a judgment post-stratification (JPS) sampling scheme. Different proportion estimators are considered, among which some are specifically designed to deal with JPS samples with empty strata; and asymptotic normality is established for each. A Monte Carlo simulation study and two examples using data from medical studies are employed to examine the performance of these proportion estimators under both perfect and imperfect ranking and for JPS data both with and without empty strata. It is shown that the JPS scheme improves estimation of the population proportion in a very wide range of settings as compared to simple random sampling (SRS). Also, findings about the relative performance of the different estimators are provided to help practitioners determine which estimator should be used under certain situations.

For various reasons individuals in a sample survey may prefer not to confide to the interviewer the correct answers to certain potentially sensitive questions such as the illegal use of drugs, illegal earning, or incidence of acts of domestic violence, etc. In such cases the individuals may elect not to reply at all or to reply with incorrect answers. The resulting evasive answer bias is ordinarily difficult to assess. The use of a randomized response method for estimating the proportion of individuals possessing those sensitive attributes can potentially eliminate the bias. Following Chaudhuri and Dihidar (2014) and Dihidar (2016), here, as a possible variant, we have made an attempt to estimate the sensitive population proportion using a combination of binomial and hypergeometric randomized responses by direct and inverse mechanism. Along with the traditional simple random sampling, with and without replacement, we consider here sampling of respondents by unequal probabilities. Essential theoretical derivations for unbiased estimator, variance and variance estimators are presented for several sampling schemes. A numerical illustration is performed to make a comparative study of the relative efficiencies of the direct and inverse mechanism.

BACKGROUND: Healthcare costs and poverty are significant barriers to achieving universal access to healthcare. Thus, Community-Based Health Insurance Schemes (CBHIS) are regarded as an influential instrument for providing access to healthcare. For this purpose, this study was carried out in order to assess the community’s Willingness to Pay (WTP) for CBHIS and its determinants among the residents of Lahore City.METHODS: A cross-sectional study was adopted during the period of May 2018 to August 2018 to conduct a standardized questionnaire survey among targeted population of Lahore. A total of 250 households from lower, middle and upper-middle-class areas were approached randomly from which 200 participated in the survey, rendering a response rate of 90.9%. Sample size was determined by using single population proportion formula assuming 5% margin of error and 95% Confidence Interval (CI). Moreover, multiple regression analysis, Pearson’s correlation and t-test were employed to determine relationships between different variables affecting WTP.RESULTS: Sixty-four percent of the respondents were willing to pay for CBHIS. Among the remaining thirty-six% of unwilling the community, income level (p< 0.05, CI=0.34 to 1.11) and education level (p< 0.05, CI=0.52-1.37) were significant predictors of WTP. Moreover, strong positive relation (p

Stimulant abuse is a major contributor to HIV transmission in the United States, yet HIV prevalence among persons who use illicit stimulants remains unknown. We implemented respondent driven sampling (RDS) to estimate the prevalence of HIV infection in this high-risk population. We also examined RDS-adjusted rates of risk behaviors among HIV-positive and HIV-negative participants. Recruited from seven seeds, our sample of 387 participants was 46% female, 89% African American, and 45.94 years old on average. Participants were predominantly non-injection cocaine users, had large networks of stimulant users, and reported an established relationship with their recruiter. The adjusted population proportion of HIV infection was 0.07 (0.04, 0.11). The majority of sexually active participants reported engagement in risk behaviors (73%), but rates generally did not differ by HIV status. Our results highlight that stimulant use is a risk factor for HIV infection. This study also demonstrates that RDS is a very effective strategy for reaching stimulant users in the community.

We derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis tests can be written in terms of linear constraints, and for exchangeable data can always be expressed as a function of the empirical distribution. Using this structure, we prove a 'Neyman-Pearson lemma' for binomial data under DP, where the DP-UMP only depends on the sample sum. Our tests can also be stated as a post-processing of a random variable, whose distribution we coin ''Truncated-Uniform-Laplace'' (Tulap), a generalization of the Staircase and discrete Laplace distributions. Furthermore, we obtain exact $p$-values, which are easily computed in terms of the Tulap random variable. Using the above techniques, we show that our tests can be applied to give uniformly most accurate one-sided confidence intervals and optimal confidence distributions. We also derive uniformly most powerful unbiased (UMPU) two-sided tests, which lead to uniformly most accurate unbiased (UMAU) two-sided confidence intervals. We show that our results can be applied to distribution-free hypothesis tests for continuous data. Our simulation results demonstrate that all our tests have exact type I error, and are more powerful than current techniques., 25 pages before references; 39 pages total. 8 figures. arXiv admin note: text overlap with arXiv:1805.09236

Alcoholism has continually posed health challenges in many communities for decades. In this paper, a more realistic model for health related risks associated with alcoholism is formulated. It considers a population proportion that has social cultural protection from alcohol consumption. In the context of this paper, such protection emanates from religious beliefs. The Next Generation Matrix (NGM) approach is used to compute the basic risk reproduction number. The risk free equilibrium point is proved to be globally asymptotically stable whenever the basic risk reproduction is less than unity and unstable otherwise. The sensitivity analysis of the basic risk reproduction number and numerical simulation results reveal that for effective control of the health risk problem in the community, the deliberate intervention strategies and policies should focus on discouraging alcoholic behaviors on its onset during initiation stage than focusing other population proportions already at risk.

For the reliability and general ability of the results of any epidemiological or medical research study, adequate number of study units is extremely important. Study of both less than needed and unnecessarily large sample size is ethically and economically unfair. Considering the importance of sample size, its determination and justification in all kinds of epidemiological or medical research studies, we propose simple and non-technical explanation to the available sample size calculation methods. In this review we covered most frequently encountered study designs in medical research. Present review provides statistical formulas for the sample size calculation of the research studies with varying objectives such as estimation of population proportion(s) and hypothesis testing, estimation of population mean, estimation of diagnostic accuracy, estimation of association and reliability, sample size calculation for case control studies, and sample size calculation for cohort studies. Limited technical details and explanations of underlying theoretical assumption for each method have been included to ensure the adaptability of the method with minimal theoretical understating and statistical knowledge.

The coordination relationship between land urbanization and population urbanization is crucial for achieving sustainable development under economic transition. Moreover, the balance between land urbanization and population urbanization is essential to guarantee the urbanization process of an entire city. This paper empirically analyzes the interaction between land urbanization and population urbanization in Nanchang from 2002 to 2017 based on the coupling coordination model (CCM). The impacts of the coordination degree on coordinated development are quantified by multivariate linear regression (MLR). The results show the following: (1) The indices of land urbanization and population urbanization in Nanchang showed an upward trend, and therefore the coordination degree in Nanchang increased significantly from 2002 to 2017. (2) The coordinated development of urbanization underwent two stages: disordered and moderately disordered. (3) The urban population proportion and the supporting capability of agricultural production had a positive impact on coordinated development. Meanwhile, the results also show that per capita education expenditures and the per capita public green area had negative impacts on the coordination degree, while economic development and the urban industrial structure were positive contributors to the coordination degree. Finally, this paper proposes that policies should be formulated to achieve coordinated development of urbanization. It can be concluded that the results regarding coordinated development of urbanization can help decision makers formulate effective measures to achieve coordinated development in the future.

BackgroundUnpremeditated injuries are the leading causes of morbidity and mortality in pediatrics population, especially in low and middle-income countries. Giving immediate help for an injured child is a crucial step for saving the child from further disability and/or death. This study aimed to assess the determinant factors of first aid knowledge and basic practice among elementary school teachers in Debre Tabor, Ethiopia.MethodInstitution based cross-sectional study was employed in Debre Tabor City. Single population proportion formula was used for sample size calculation and a total of 216 elementary school teachers were included in study. Simple random sampling technique with proportional allocation was applied for selections of the study participant. Data entry was done by Epi data version 3.1 and the data was exported to SPSS version 21 for analysis. Binary and multivariable logistic regression analysis were performed to identify determinants of knowledge on first aid. Crude and adjusted odds ratios were used to determine the significance and strength of association at 95% confidence interval.ResultOur study revealed that 45.8% of the subjects were knowledgeable on first aid. More than 75% of study participant reported that they have encountered a child who need first aid. Among this 64% of them provide first aid. The multivariable analysis revealed that service year (AOR=3.51, 95%CI: (1.06, 11.59)), educational status (AOR=12.15, 95%CI: (3.17, 46.67)), previous first aid training (AOR=0.43, 95%CI: (0.21, 0.87)) and information about first aid (AOR=0.12, 95%CI ;(0.03, 0.48)) were found to be significantly associated with having knowledge on first aid.ConclusionSchool teachers have low knowledge on first aid. Educational status, service year, previous first aid training and information on first aid were the predictor of first aid knowledge. Introducing essential first aid training in the curriculum during teachers’ training shall be considered.

In this paper, proportion estimators and associated variance estimators are proposed for a binary variable with a concomitant variable based on modified ranked set sampling methods, which are extreme ranked set sampling (ERSS), median ranked set sampling (MRSS), percentile ranked set sampling (Per-RSS) and L ranked set sampling (LRSS) methods. The Monte Carlo simulation study is performed to compare the performance of the estimators based on bias, mean squared error, and relative efficiency for different levels of correlation coefficient, set and cycle sizes under normal and log-normal distributions. Moreover, the study is supported with real data application.

Objective Most neonatal deaths occur in low income and middle-income countries and about half of the deaths occur at home. It is estimated that about 75% of neonatal deaths could be avoided with simple, low-cost tools that already exist such as antibiotics for pneumonia and sepsis, sterile blades to cut the umbilical cords using knit caps and kangaroo care to keep babies warm. The aim of this study is to assess the knowledge, attitudes, and practices of newborn care among postnatal mothers at Bahir Dar, Ethiopia 2016. An institutional based cross-sectional study design was used. The sample size was calculated by using a single population proportion formula. The total sample size was 422. The collected data was coded and entered to Epi-Data version 3.1 and exported and analyzed using SPSS version 23.0. Both descriptive and multivariate logistic regression was performed. Result A total of 414 postnatal mothers were interviewed with a response rate of 98.1%, among them 55.3% had good knowledge and 60.6% had a good practice of newborn care. Age of the mother, occupation, the month of pregnancy at first ANC visits, overall knowledge and attitude level was found to have a significant association with newborn care practice.

(1) Background: Human mobility between geographic units is an important way in which COVID-19 is spread across regions. Due to the pressure of epidemic control and economic recovery, states in the United States have adopted different policies for mobility limitations. Assessing the impact of these policies on the spatiotemporal interaction of COVID-19 transmission among counties in each state is critical to formulating epidemic policies. (2) Methods: We utilized Moran’s I index and K-means clustering to investigate the time-varying spatial autocorrelation effect of 49 states (excluding the District of Colombia) with daily new cases at the county level from 22 January 2020 to 20 August 2020. Based on the dynamic spatial lag model (SLM) and the SIR model with unreported infection rate (SIRu), the integrated SLM-SIRu model was constructed to estimate the inter-county spatiotemporal interaction coefficient of daily new cases in each state, which was further explored by Pearson correlation test and stepwise OLS regression with socioeconomic factors. (3) Results: The K-means clustering divided the time-varying spatial autocorrelation curves of the 49 states into four types: continuous increasing, fluctuating increasing, weak positive, and weak negative. The Pearson correlation analysis showed that the spatiotemporal interaction coefficients in each state estimated by SLM-SIRu were significantly positively correlated with the variables of median age, population density, and proportions of international immigrants and highly educated population, but negatively correlated with the birth rate. Further stepwise OLS regression retained only three positive correlated variables: poverty rate, population density, and highly educated population proportion. (4) Conclusions: This result suggests that various state policies in the U.S. have imposed different impacts on COVID-19 transmission among counties. All states should provide more protection and support for the low-income population, high-density populated states need to strengthen regional mobility restrictions, and the highly educated population should reduce unnecessary regional movement and strengthen self-protection.

ObjectiveTo evaluate COVID-19 infection and mortality disparities in ethnic and racial subgroups in a state-wise manner across the USA.MethodsPublicly available data from The COVID Tracking Project at The Atlantic were accessed between 9 September 2020 and 14 September 2020. For each state and the District of Columbia, % infection, % death, and % population proportion for subgroups of race (African American/black (AA/black), Asian, American Indian or Alaska Native (AI/AN), and white) and ethnicity (Hispanic/Latino, non-Hispanic) were recorded. Crude and normalised disparity estimates were generated for COVID-19 infection (CDI and NDI) and mortality (CDM and NDM), computed as absolute and relative difference between % infection or % mortality and % population proportion per state. Choropleth map display was created as thematic representation proportionate to CDI, NDI, CDM and NDM.ResultsThe Hispanic population had a median of 158% higher COVID-19 infection relative to their % population proportion (median 158%, IQR 100%–200%). This was followed by AA, with 50% higher COVID-19 infection relative to their % population proportion (median 50%, IQR 25%–100%). The AA population had the most disproportionate mortality, with a median of 46% higher mortality than the % population proportion (median 46%, IQR 18%–66%). Disproportionate impact of COVID-19 was also seen in AI/AN and Asian populations, with 100% excess infections than the % population proportion seen in nine states for AI/AN and seven states for Asian populations. There was no disproportionate impact in the white population in any state.ConclusionsThere are racial/ethnic disparities in COVID-19 infection/mortality, with distinct state-wise patterns across the USA based on racial/ethnic composition. There were missing and inconsistently reported racial/ethnic data in many states. This underscores the need for standardised reporting, attention to specific regional patterns, adequate resource allocation and addressing the underlying social determinants of health adversely affecting chronically marginalised groups.

In the traditional game theory, a widely accepted assumption is that the participants are completely rational and under the condition of complete information. But in the realistic economy experiences, the participants’ conditions of complete rationality and information are usually hard to be fulfilled. The mutations, un-fixed mechanisms, and policy variations usually challenge the process of natural game evolution. In this work, we mainly study how to make the iterative transformation of policy updating rules to maximize their own benefits in the case of heterogeneous updating rules. In particular, a novel mutation mechanism is developed to study the cooperation situation in natural selection by introducing two different proportion groups in the population, one is based on imitation, the other is based on aspiration level, and both proportions can transform each other under certain conditions at the end of each generation. The mutation of the individual mechanism may occur, it is found that the population proportion and individual rule mutation rate have a strong stabilizing effect on population cooperation under this mixed mechanism, and the lower aspiration level has a certain promoting effect on cooperation as well.

This paper shows that an important class of evolutionary game - theoretic models ? those in which agents form beliefs about the behavior of others on the basis of samples they observe from the population ? violate a property ? monotonicity ? that many authors have argued any well-specified evolutionary model should possess. A stripped down evolutionary model that closely follows Young?s (Econometrica, 1993) pioneering model is developed, and a theorem is presented showing that the sampling process on which beliefs are based necessarily generates a violation of monotonicity. (Loosely, a violation of monotonicity means that the population proportion of a "less fit" strategy grows more quickly than the population proportion of a "more fit" strategy.) A numerical example illustrating this violation is also presented. This violation does not imply that models with sampling-based beliefs are defective or implausible in any way. On the contrary, these models are built on carefully articulated and justified microfoundations. What this paper demonstrates is that analyses that begin with an assumption of monotonicity, without the specifics of the dynamic process explicitly stated, are not applicable to all evolutionary models.

This article focuses on the improvement of a well-celebrated randomized response technique of Kuk. A generalized randomized response technique is suggested. In particular, the generalized geometric distribution of order k is introduced as a randomization device for estimating the population proportion of a rare sensitive attribute. The proposed randomized response technique includes Singh and Grewal and Hussain et al. techniques as its special cases. Through numerical illustrations, it is established that the suggested technique is superior to the Kuk, Singh and Grewal, and Hussain et al. techniques. Flexibility of the proposed technique is also discussed.

In this paper we derive a bound for the variance of unbiased estimator of the finite population proportion under inverse sampling without replacement.

In this paper, we consider the problem of estimating the population proportion in pair ranked set sampling design. An unbiased estimator for the population proportion is proposed, and its theoretical properties are studied. It is shown that the estimator is more (less) efficient than its counterpart in simple random sampling (ranked set sampling). Asymptotic normality of the estimator is also established. Application of the suggested procedure is illustrated using a data set from an environmental study.

From the perspective of long-term equilibrium, the proportion of a region’s economy and population in the country should roughly be equal. In this paper, the quotient of GDP proportion and population proportion is defined as R, whose value and characteristics of volatility accurately reflects the feature of distribution and equilibrium between economy and population. By using GIS visualization technology, this paper finds that the economic and demographic distribution in Chins is still far from matching currently, with a trend of polarization between east and west. However, from 2000 to 2015, the matching degree of economy and population at the national level is actually on the rise. This paper then divides apart the economic factor and demographic factor that cause the R value to change, and comes to a conclusion that the status between the economy and the population in most provinces is affected by economic factor to a greater extent, and the role of population factor is relatively minor.

This paper proposed alternative beta estimators of the population proportion of a sensitive attribute when life data were obtained through the administration of survey questionnaires on abortion of some matured women. The results showed that the proposed alternative beta estimators were more efficient in capturing responses from respondents than the simple beta estimator proposed by Winkler and Franklin for relatively small, medium as well as large sample sizes respectively.

This article purposes the estimation of population proportion of a sensitive attribute through randomized response technique. An efficient estimator is suggested using six decks of cards to randomise the response. Many existing models can now be viewed as the special case of the proposed model. The superiority of the proposed procedure is established through numerical calculation of percentage relative efficiency with prominent competitors. The proposed procedure is also studied under stratified random sampling protocol. In addition, it is shown that, the proposed stratified estimator, performs better in term of efficiency than its only existing two deck stratified competitor.

Background Limit of detection (LOD) is an important performance characteristic of clinical laboratory tests. Verification, as recommended by the CLSI EP17-A2 guideline, is done by testing a sample with a claimed LOD concentration. Claimed LOD is verified if the 95% CI for the population proportion, calculated from observed proportion of positive results, contains the expected detection rate of 95% (CLSI EP17-A2; Clin Chem 2004;50:732–40). Claimed LOD, verification sample concentration, and observed rate of positive results are subjects to systematic and random errors that can cause false failure or false acceptance of the LOD verification. The aim of this study was to assess the probability to pass or fail verification of claimed LOD with various numbers of tests as function of the ratio of test sample concentration and actual LOD for PCR-based molecular diagnostics tests and provide recommendations for study design. Methods A method of calculating the probability of passing the claimed LOD verification following CLSI EP17-A2 guideline recommendations, based on the Poisson–binomial probability model, have been developed for PCR-based assays. Results Calculations and graphs have shown that the probability of passing LOD verification depends on the number of tests and has local minima and maxima between 0.975 and 0.995 for the number of tests from 20 to 1000 on samples having actual LOD concentration. The probability of detecting the difference between claimed LOD and actual LOD increases with the number of tests performed. Graphs and tables with examples are included. Conclusions Method, tables, and graphs helping in planning LOD verification study in molecular diagnostics are provided along with the recommendations on what to do in case of failure to verify the LOD claim.

This paper addresses the problem of estimating the population proportion π of a sensitive group. We have suggested a randomized response (RR) model that is more efficient than the one envisaged by Gjestvang and Singh ([2006), A new randomized response model, Journal of Royal Statistcal Socity, B, (3), 523–530].

Mahalanobis distance may be used as a measure of the disparity between an individual’s profile of scores and the average profile of a population of controls. The degree to which the individual’s profile is unusual can then be equated to the proportion of the population who would have a larger Mahalanobis distance than the individual. Several estimators of this proportion are examined. These include plug-in maximum likelihood estimators, medians, the posterior mean from a Bayesian probability matching prior, an estimator derived from a Taylor expansion, and two forms of polynomial approximation, one based on Bernstein polynomial and one on a quadrature method. Simulations show that some estimators, including the commonly-used plug-in maximum likelihood estimators, can have substantial bias for small or moderate sample sizes. The polynomial approximations yield estimators that have low bias, with the quadrature method marginally to be preferred over Bernstein polynomials. However, the polynomial estimators sometimes yield infeasible estimates that are outside the 0–1 range. While none of the estimators are perfectly unbiased, the median estimators match their definition; in simulations their estimates of the proportion have a median error close to zero. The standard median estimator can give unrealistically small estimates (including 0) and an adjustment is proposed that ensures estimates are always credible. This latter estimator has much to recommend it when unbiasedness is not of paramount importance, while the quadrature method is recommended when bias is the dominant issue., Highlights • We seek an estimate of the population proportion with extreme Mahalanobis index. • Nine point estimates are examined in an extensive simulation study. • Maximum likelihood estimates have substantial bias. • Methods based on polynomial approximations give low bias, but can be out-of-range. • An adapted median estimator that always gives sensible estimates is proposed.

The objective of this study was to analyze the current situation of the ICMS-E in the Brazilian states and to estimate the consequences of its non-applicability in the state of Paraiba. Through documentary and bibliographic research, the legal provisions that institute and regulate the ICMS-E in Brazilian states were raised, such as the criteria for redistribution and their respective percentage of participation. The population criterion was used to estimate the value of ICMS-E not passed on to the municipalities of Paraiba, since the legal criteria were not regulated due to the unconstitutionality of the state law. The estimated population of the 5 most populous municipalities in the state and the 5 municipalities with the smallest population were collected, to verify the impact of the non-applicability of the ICMS-E in both realities. In the data analysis, the Population Proportion method was used, where the relative frequency with which this category is observed in the population (p) was calculated according to Mann (2005). The results showed that 17 Brazilian states instituted the ICMS-E under various criteria for the redistribution of resources, among which environmental conservation units, public water sources and solid waste treatment stand out. In Paraiba, the losses related to the non-applicability of the ICMS-E in the analyzed period add up to approximately 845 million reais. Thus, the poorest 5 municipalities stopped receiving an average of 430 thousand reais / year. It is concluded, therefore, that the ICMS-E is an important tax mechanism for environmental management capable of stimulating the conservation of the environment.

Problem setting. For wider involvement of investors, it is necessary to provide them with information about community resources, including local human resources. A part of population that offers their labor for manufacturing goods and providing different services is the so-called “economically active population”. According to the classification of the International Labor Organization, economically active population includes citizens of both genders, aged 15 to 70, who are engaged in economic activities or are looking for job and ready to work. For qualitative cooperation with potential investors the local authorities should have, inter alia, information about estimated number of citizens at the age of economically active population. Recent research and publications analysis. A manual “Planning for the development of the territorial communities” suggests to form “a community profile” which discloses the causes and consequences of changes in population age structure of a certain territory. Such “profiles” were prepared for several Ukrainian cities during implementation of the project “Evidence-Based Economic Development Planning in Ukraine” (EBED). In particular, they show the trends of demographic changes, the results of urban population structure forecast until 2030. There are still very few similar studies at the level of cities and regions. Highlighting previously unsettled parts of the general problem. The article describes methods and results of its use for forecasting the population structure in different age groups, especially at the age of economically active population. The purpose of the study is to compare trends of changes in population structure in Lviv Region districts. Paper main body. The duration of evaluated period depends on the purpose of forecasting. In our opinion the evaluated period should be at least 20 years. Unlike the approach, used in EBED project, the proposed methods and corresponding model operate with 5-year population cohorts, that reduces the complexity of initial data inputting. In addition, the proposed approach uses coefficients of changes in the number of age groups, which are calculated by the ratio of population number in adjacent cohorts after 5 years. Age structure of their population, mortality rate in age groups and migration processes cause different rates of changes in the number of separate age groups. Namely, the number of people at the age of economically active population will have different changes in Lviv Region districts in 20 years’ time. As an example, in Pustomytiv District the number of people in the age group 15 to 70 is expected to increase (by 6,5%), which covers the economically active population. In other districts the number of this population group will reduce, in particular the most in Zhydachiv District (by19,6%). Simultaneously with a decrease in the number of economically active population in Lviv Region districts, the part of people aged 70 and more will increase and the part of people under the age of 15 will decrease. As a result, we will have changes in the ratio of the number of people at the age of economically active population to the number of persons of other age groups. These results prove that there will be negative changes in population structure of all Lviv Region districts in 20 years’ time. The most intensively they will occur in Stryi (excluding Stryi city), Drohobych (excluding Drohobych, Boryslav and Truskavets cities), Sambir (without Sambir city) and Starosambirsk Districts: changes in the ratio of the number of potential economically active population to other age groups here will exceed 15%. These ratios will remain the smallest in Turka and Peremyshliany Districts (in 2038 they will be respectively 2,05 and 2,09). The biggest changes will happen in Truskavets city – the ratio will reduce by as much as 28%. The obtained results indicate that in districts and cities of Lviv Region, the population structure is changing dynamically, mainly in the direction of reducing the population proportion, whose responsibility is to bring up children and support elderly people. Conclusions of the research and prospects for further studies. Using these methods of forecasting, based on 5-year cohorts, has allowed identifying future changes in population number of Lviv Region, who, according to their age, correspond to economically active population. In all districts and cities of the regional significance, the ratio of potential economically active population to other age groups will significantly reduce. It is necessary to place the results of forecasts in strategies, explanatory notes to general plans of settlements, city passports and community profiles, etc. This will allow substantiating the planning of local economic and spatial development of the territories.

Summary Respondent-driven sampling is an approach for estimating features of populations that are difficult to access using standard survey tools, e.g., the fraction of injection drug users who are HIV positive. Baraff et al. (2016) introduced an approach to estimating uncertainty in population proportion estimates from respondent-driven sampling using the tree bootstrap method. In this paper we establish the consistency of this tree bootstrap approach in the case of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$m$\end{document}-trees.

Patient self-referral is a process through which patients refer themselves to higher level health facilities without seeing anyone else first or being advised to refer themselves by a health professional. Despite the expansion in the number of health facilities, this phenomenon is perceived when patients routinely access referral hospitals. This study aimed to determine the magnitude and identify the determinants of outpatient self-referral at referral hospitals. It was conducted in East Wollega zone of Oromia National Regional State, Ethiopia. A cross-sectional study design was used to collect data between December 1 and 30, 2017. For the study, a 404 samples size was determined using a single population proportion formula. Data entry and analysis were done using SPSS version 20. Descriptive statistics, binary and multiple logistic regressions were performed. A total of 404 outpatients were included, thereby making the response rate of 96.8%. Amongst the 391 outpatients who were interviewed, 330 (84.4%) engaged in self-referral. The factors significantly associated with outpatient self-referral were referral information (Adjusted odds ratio and 95% confidence interval (CI) = 0.32 [0.15–0.70]), illness severity (Adjusted odds ratio and 95% CI = 3.50 [1.47–8.30]), confidence of patients in getting care providers (Adjusted odds ratio and 95 CI = 3.03 [1.51–6.07]), availability of laboratory services (Adjusted odds ratio and 95% CI = 5.00 [2.20–11.23]) and drugs (Adjusted odds ratio and 95% CI = 2.37 [1.01–5.53]) and quality of health services (Adjusted odds ratio and 95% CI = 3.00 [1.42–6.33]). The proportion of outpatient self-referral was high and it was associated with referral information, patient confidence in getting healthcare providers, the severity of illness, availability of laboratory services, drugs and the quality of services. A monitoring system of the referral linkage of health facilities should be established at all levels and health facilities should create awareness in the community regarding the referral linkages of health facilities.

This article studies the properties of the maximum likelihood estimator of the population proportion in ranked set sampling with extreme ranks. The maximum likelihood estimator is described and its asymptotic distribution is derived. Finite sample size properties of the estimator are investigated using simulation studies. It turns out that the proposed estimator is substantially more efficient than its simple random sampling and ranked set sampling analogs, as the true population proportion tends to zero/unity. The method is illustrated using data from the National Health and Nutrition Examination Survey.

Objective: To determine the prevalence and associated factors with the maternal delay in seeking emergency obstetrics services among pregnant women, Arsi Zone, Oromiya, Ethiopia, 2016.Methods: A Facility based Cross-sectional study design using a quantitative method was conducted at public health facilities of Arsi Zone. Sample size, 847 was determined using a single population proportion formula. A total of 10 health centers which provide obstetric care selected randomly and sample size proportionally allocated to each facility. Data entered in Epi Info version 3.3.2 software and exported to SPSS version 20 for statistical analysis. p

Using a sample from a population to estimate the proportion of the population with a certain category label is a broadly important problem. In the context of microbiome studies, this problem arises when researchers wish to use a sample from a population of microbes to estimate the population proportion of a particular taxon, known as the taxon's relative abundance. In this paper, we propose a beta-binomial model for this task. Like existing models, our model allows for a taxon's relative abundance to be associated with covariates of interest. However, unlike existing models, our proposal also allows for the overdispersion in the taxon's counts to be associated with covariates of interest. We exploit this model in order to propose tests not only for differential relative abundance, but also for differential variability. The latter is particularly valuable in light of speculation that dysbiosis, the perturbation from a normal microbiome that can occur in certain disease conditions, may manifest as a loss of stability, or increase in variability, of the counts associated with each taxon. We demonstrate the performance of our proposed model using a simulation study and an application to soil microbial data.