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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]

In data analysis, we cannot expect the data under study to always follow a symmetric probability distribution; they can have a skewed probability distribution. Modeling skewed data is a challenging task for data scientists. A mixture of probability distributions is a better option for modelling skewed data. In this study, we generated a few mixtures of probability distributions using the exponential as the first fixed component and Gompertz, Lindley, and log-normal distributions as the second component for modelling skewed data. We also examined the characteristics of mixed probability distributions. The maximum likelihood method was used to estimate the unknown parameters. As a result, all three mixture models have a right-skewed pattern, which provides a better fit than existing distributions. Finally, we used real-time datasets to model skewed data. [ABSTRACT FROM AUTHOR]

Specification of a parametric model for the intensity function is a fundamental task in statistics for spatial point processes. It is, therefore, crucial to be able to assess the appropriateness of a suggested model for a given point pattern dataset. For this purpose, we develop a new class of semiparametric goodness-of-fit tests for the specified parametric first-order intensity, without assuming a full data generating mechanism that is needed for the existing popular Monte Carlo tests. The proposed tests crucially rely on accurate nonparametric estimation of the second-order properties of a point process. To address this we propose a new nonparametric pair correlation function (PCF) estimator for clustered spatial point processes under some mild shape constraints, which is shown to achieve uniform consistency. The proposed test statistics are computationally efficient owing to closed-form asymptotic distributions and achieve the nominal size even for testing composite hypotheses. In practice, the proposed estimation and testing procedures provide effective tools to improve parametric intensity function modeling, which is demonstrated through extensive simulation studies as well as a real data analysis of street crime activity in Washington DC. for this article are available online. [ABSTRACT FROM AUTHOR]

Currently, two-level Mokken scale analysis for clustered test data is being developed. This paper contributes to this development by providing model-fit procedures for two-level Mokken scale analysis. New theoretical insights suggested that the existing model-fit procedure from traditional (one-level) Mokken scale analyses can be used for investigating model fit at both level 1 (respondent level) and level 2 (cluster level) of two-level Mokken scale analysis. However, the traditional model-fit procedure requires some modifications before it can be used at level 2. In this paper, we made these modifications and investigated the resulting model-fit procedure. For two model assumptions, monotonicity and invariant item ordering, we investigated the false-positive count and the sensitivity count of the level 2 model-fit procedure, with respect to the number of model violations detected, and the number of detected model violations deemed statistically significant. For monotonicity, the detection of model violations was satisfactory, but the significance test lacked power. For invariant item ordering, both aspects were satisfactory. [ABSTRACT FROM AUTHOR]

Rayleigh–Taylor (RT) interfacial mixing plays an important role in nature and technology, including atmospheric flows. In this work, we identify the physics properties of Rayleigh–Taylor mixing through the analysis of unprocessed experimental data. We consider the fluctuations spectra of the specific kinetic energy of each of the velocity components, and identify their spectral shapes, by employing the group theory guided foundations and the rigorous statistical method. We find the spectral shape parameters, including their mean values and relative errors, and apply the Anderson–Darling test to inspect the residuals and the goodness-of-fit. We scrupulously study the effect of the fitting window and identify, for each velocity component, the best fit interval, where the relative errors are small and the goodness of fit is excellent. We reveal that the fluctuations spectra in RT mixing experiments can be described by a compound function, being a product of a power-law and an exponential. The data analysis results unambiguously discovered the dynamic anisotropy and the dynamic bias of RT mixing and displayed the necessity to improve the design of experiments on RT mixing. [ABSTRACT FROM AUTHOR]

In the literature of modern psychometric modeling, mostly related to item response theory (IRT), the fit of model is evaluated through known indices, such as χ2, M2, and root mean square error of approximation (RMSEA) for absolute assessments as well as Akaike information criterion (AIC), consistent AIC (CAIC), and Bayesian information criterion (BIC) for relative comparisons. Recent developments show a merging trend of psychometric and machine learnings, yet there remains a gap in the model fit evaluation, specifically the use of the area under curve (AUC). This study focuses on the behaviors of AUC in fitting IRT models. Rounds of simulations were conducted to investigate AUC's appropriateness (e.g., power and Type I error rate) under various conditions. The results show that AUC possessed certain advantages under certain conditions such as high-dimensional structure with two-parameter logistic (2PL) and some three-parameter logistic (3PL) models, while disadvantages were also obvious when the true model is unidimensional. It cautions researchers about the dangers of using AUC solely in evaluating psychometric models. [ABSTRACT FROM AUTHOR]

Simple Summary: The current study was conducted to predict the live body weight using body length, heart girth, rump height and withers height of 173 Savanna goats from a stud breeder at Bysteel, Polokwane municipality, South Africa. A multivariate adaptive regression splines algorithm was used, along with the different proportions of the test and training sets to predict body weight. The body weight was best predicted from the training dataset with body weight influenced by withers height and heart girth, respectively. The interaction of withers height and body length with withers height and heart girth also influenced body weight. In conclusion, it could be suggested that the multivariate adaptive regression splines algorithm might allow Savanna goat breeders to find the best population and examine the body measurements affecting body weight as indirect selection criteria for describing the breed description of Savanna goats and aiding sustainable meat production. The Savanna goat breed is an indigenous goat breed in South Africa that is reared for meat production. Live body weight is an important tool for livestock management, selection and feeding. The use of multivariate adaptive regression splines (MARS) to predict the live body weight of Savanna goats remains poorly understood. The study was conducted to investigate the influence of linear body measurements on the body weight of Savanna goats using MARS. In total, 173 Savanna goats between the ages of two and five years were used to collect body weight (BW), body length (BL), heart girth (HG), rump height (RH) and withers height (WH). MARS was used as a data mining algorithm for data analysis. The best predictive model was achieved from the training dataset with the highest coefficient of determination and Pearson's correlation coefficient (0.959 and 0.961), respectively. BW was influenced positively when WH > 63 cm and HG >100 cm with a coefficient of 0.51 and 2.71, respectively. The interaction of WH > 63 cm and BL < 75 cm, WH < 68 cm and HG < 100 cm with a coefficient of 0.28 and 0.02 had a positive influence on Savanna goat BW, while male goats had a negative influence (−4.57). The findings of the study suggest that MARS can be used to estimate the BW in Savanna goats. This finding will be helpful to farmers in the selection of breeding stock and precision in the day-to-day activities such as feeding, marketing and veterinary services. [ABSTRACT FROM AUTHOR]

Orientation: Ethical leadership is crucial in fostering work engagement among employees in organisations. Research purpose: This study aimed to empirically validate a theoretical model explicating the structural relationships between ethical leadership, ethical climate and work engagement. Motivation for the study: The central role of work engagement in sustaining competitive advantage calls for an analysis of the role of ethical leadership and climate in enhancing an engaged workforce. Research approach/design and method: A non-probability convenience sample consisting of 304 participants was drawn from 10 selected private security companies. Main findings: High levels of reliability were found, and the unidimensionality of the subscales was confirmed through exploratory factor analyses. A good fit with the data was found for the measurement models through confirmatory factor analysis. Structural equation modelling showed a reasonable fit for the structural model. Positive relationships were found between ethical leadership, climate and work engagement. Practical/managerial implications: The findings emphasise the role of ethical leadership and climate in work engagement. Ethical leadership fosters work engagement if employees perceive their leaders as ethical and if there is provision of favourable, transparent policies and procedures. Contribution/value-add: Ethical leadership alone may not be a sufficient condition for employee work engagement; other variables such as a positive ethical climate also play a role. The study suggests specific variables that may also combine with leadership to positively influence work engagement. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a new probability distribution named as inverse power Maxwell distribution. The proposal distribution can be seen as an extension of the Maxwell distribution with more flexibility in modeling upside-down lifetime data. Some statistical properties of this distribution are derived. In estimation viewpoint, five methods are used for estimating the unknown parameters of the distribution and these methods are performed through the simulation study. Finally, two real data sets were analyzed to illustrate the applicability of the proposed distribution, proving that it fits each real data set much better than some other existing distributions. [ABSTRACT FROM AUTHOR]

To develop a mechanistic-empirical pavement design system for Norwegian conditions, this paper evaluates the influence of the adoption of different models and shifting techniques on the determination of dynamic modulus master curves of asphalt mixtures. Two asphalt mixture types commonly used in Norway, namely Asphalt Concrete (AC) and Stone Mastic Asphalt (SMA) containing neat bitumen and polymer-modified bitumen, were prepared by the roller compactor, and their dynamic moduli were determined by the cyclic indirect tensile test. The dynamic modulus master curves were constructed using the standard logistic sigmoidal model, a generalized logistic sigmoidal model and the Christensen–Anderson–Marasteanu model. The shifting techniques consisted of log-linear, quadratic polynomial function, Arrhenius, William–Landel–Ferry and Kaelble methods. The absolute error, normalised square error and goodness-of-fit statistics encompassing standard error ratio and coefficient of determination were used to appraise the models and shifting methods. The results showed that the standard logistic sigmoidal model and the Williams–Landel–Ferry equation had the most suitable fits for the specimens tested. The asphalt mixtures containing neat bitumen had a better fit than the ones containing polymer-modified bitumen. The Kaelble equation and log-linear equation led to similar results. These findings provide a relevant recommendation for the mechanistic-empirical pavement design system. [ABSTRACT FROM AUTHOR]

The Cramer-von Mises test is commonly used to determine how well-observed sample data fits a given model. The existing Cramer-von Mises test under traditional statistics is commonly used when sample data in reliability work are resolute and precise. In this paper, we introduced a Neutrosophic Cramer-von Mises (NCVM) test under neutrosophic statistics. The necessary measures and procedures are presented to perform the test. For the application purpose, we consider the real-life data sets of failure time batteries and ball bearings. It is inferred that the NCVM test is more instructive than the classical CVM test under indeterminacy. [ABSTRACT FROM AUTHOR]

The taper-volume relationship is an essential tool for planning silvicultural management in forests with the final aim of promoting the distribution of products. The objective of this study is the generation of a compatible model that allows an accurate estimation of the taper-volume of Abies religiosa in several regions of Mexico. A data set of 2608 values was considered for the analysis of the information; the model was simultaneously adjusted by seemingly unrelated regression (SUR) for the estimation of compatible parameters. The model generated coefficients of determination with fit levels higher than 97 %, roots mean square less than 0.40, biases lower than 0.11, with certainty to model each forest region, which are complemented with their respective Akaike information criteria (AIC). In most cases, the shape factor of the species went from neiloid to paraboloid. This information will be useful for timber forest inventories. [ABSTRACT FROM AUTHOR]

In this article, a new class of weighted exponential distribution called Entropy-Based Exponential weighted distribution (EBEWD) is proposed. The main idea of the new lifetime distribution is in using the Shannon entropy measure as a weighted function. The mathematical properties of the EBEWD, such as reliability measures, moment measures, variability measures, shapes measures, entropy measures and Fisher's information, were derived. The unknown parameters of the proposed distribution were estimated using the maximum likelihood estimation method. The efficiency and flexibility of the EBEWD were examined numerically and then by a real-life data application. The results revealed that the EBEWD outperforms some existing distributions in terms of their test statistics. [ABSTRACT FROM AUTHOR]

It is of great interest for establishments that offer a product or service, for example museums, to know the number of possible visits as a function of other variables that customers will make in a specific period. This to evaluate the degree of demand that exists and at the same time, evaluate if the dissemination strategies are working or otherwise, make more appropriate decisions to improve the quality of attention and satisfaction with visitors. To implement the generalized linear model to estimate the number of annual visits to museums in Mexican territory as a function of predictive variables, a database of 110 museums taken from the Instituto Nacional de Estadística y Geografía (INEGI) for the years 2017 and 2018 was used. The models used were regression ordinary linear (RLO) and Poisson regression (RP) and these were applied to all the principal components of eleven predictor variables (web page, reception and service capacity, main theme, permanent collection, ownership, entry, adult fee, discounts, type of visits, open days of the year and temporary exhibitions) to counteract multicollinearity. Besides, the coefficient of determination (R²) was measured between the observed and estimated data to determine the method with the best fit. The functions were used to estimate the number of visits for the years 2019 and 2020. With the model that best fit, an analysis of estimation errors was performed. Comparing the observed data for the years 2017 and 2018 with the results estimated with the characteristic functions of each model, the determination coefficients were R² = 0.61 for the RLO and R² = 0.86 for the PR, respectively. For the years 2019 and 2020, the coefficients of determination obtained were R² = 0.68 and R² = 0.31 for the RLO, and R² = 0.87 and R² = 0.84 for the RP, respectively. The maximum error of estimation registered was between 10 001 and 20 000 annual visits. It is shown that the most suitable model to forecast future annual visits to any museum in Mexico is the Poisson regression. It is believed that the high adjustment to the data observed with the PR method is because these did not have an excess of zeros and fulfilled the assumption of equidispersion. Finally, with the proposed characteristic function, the number of annual visits can be estimated with a maximum error of around 10 %, which is low compared to the maximum number of annual visits that a museum receives. [ABSTRACT FROM AUTHOR]

Models for forecasting various ecosystem properties have great potential that comes with a need for model validation. Before we can perform such validation, we need to define what it means for the model to perform well, which depends on the question being asked. Often, it seems easy to ignore the model question and take a standard well-known error measure for comparing the model to the available data. The question is whether this practice is adequate. Here, we defined different types of model-data mismatches that may be more or less relevant to different types of questions. We show that error measures differ in their sensitivity to the type of mismatch and robustness to sparse and noisy data. The results imply that a careful selection of error measures, using a clearly defined ecological question as a starting point, is vital to proper model evaluation. While we present our results as generally applicable to the validation of any type of forecasting model, we also illustrate them using cyanobacterial bloom modelling as a detailed example of a case where different questions could be asked of the same model. • We show the need for a well-defined model question before model evaluation. • Error measures differ with respect to the question they ask the model. • Error measures differ in their robustness to sparse and noisy data. • The choice of error measure can strongly affect the model training/validation outcome. • The above is illustrated with a detailed example of cyanobacterial bloom modelling. [ABSTRACT FROM AUTHOR]

The logit binomial logistic dose response model is commonly used in applied research to model binary outcomes as a function of the dose or concentration of a substance. This model is easily tailored to assess the relative potency of two substances. Consequently, in instances where two such dose response curves are parallel so one substance can be viewed as a dilution of the other, the degree of that dilution is captured in the relative potency model parameter. It is incumbent that experimental researchers working in fields including biomedicine, environmental science, toxicology and applied sciences choose efficient experimental designs to run their studies to both fit their dose response curves and to garner important information regarding drug or substance potency. This article provides far-reaching practical design strategies for dose response model fitting and estimation of relative potency using key illustrations. These results are subsequently extended here to handle situations where the assessment of parallelism and the proper dose-scale are also of interest. Conclusions and recommended strategies are supported by both theoretical and simulation results. [ABSTRACT FROM AUTHOR]

Among milk traits, fat-to-protein ratio (FPR) is considered a potential measure of a cow's energy status and is one of the selection criteria necessary to improve metabolic stability. Further genetic analyses require an appropriate model that describes the pattern of FPR changes throughout lactation. The objective of the study was to examine five mathematical functions to describe the lactation curve for FPR in the first three lactations of Polish Holstein-Friesians. The dataset contained FPR records for 5690 cows in the first lactation, 4081 cows in the second, and 2636 cows in the third lactation based on 48908, 34706, and 22097 test-day (TD) records, respectively. Using the MIXED procedure of SAS statistical analytics software, ten linear models (five with fixed effects only, and five with the additional random effect of cow) were fitted to the TD records. The goodness of fit was tested with Akaike's information criterion, residual variances and the correlation coefficient between the actual and estimated values. The model proposed by Ali and Schaeffer (1987) had the best fit to FPR in the first three parities, and the model of Wilmink (1987) provided the worst fit. The correlation coefficient between the actual and the estimated values of FPR was higher for models that included the random cow effect compared with models without this effect. [ABSTRACT FROM AUTHOR]

Errors in the physics schemes and parameters of a land surface model can lead to large errors/bias in simulated soil moisture. In addition, large bias in simulated soil moisture may be caused by soil lateral water flow that is not described in a land surface model. In the present study, three model output statistics (MOS) approaches (a linear regression based MOS, a rescaling based MOS and a cumulative distribution function matching based MOS) are proposed to correct these biases and errors at stations that have soil moisture observations. Results show that the biases/errors in simulated soil moisture were significantly corrected by the three MOS approaches. The best performance was obtained for the linear regression MOS model consisting of four separate linear regression MOS models for different seasons throughout the year (MOS-SN). However, for the linear regression MOS and the rescaling MOS, a few months' data may also be used for MOS correction when the same seasonal period is used for both model fitting and prediction. With respect to goodness of fit and performance, the linear regression MOS model is better than the rescaling MOS model, and the MOS-SN is slightly better than the nonlinear cumulative distribution function matching approach. For sites where soil moisture observations are much shorter, or more intermittent, than meteorological observations, the linear regression MOS approaches can be used to reconstruct missing historic soil moisture data. All MOS approaches can also be used to correct the errors/bias in forecast soil moisture from weather or climate models at sites with soil moisture observations. [ABSTRACT FROM AUTHOR]

In this article, parametric and nonparametric statistical inference analysis of a set the measurements of air pollution because of PM2.5 concentrations was performed. The research work was carried out in an urban park in Quito, Ecuador. Specifically, the park that was chosen to perform the analysis was La Carolina Park. The analysis carried out here was aimed at obtaining the statistical models for parts of this urban park under study and some of its border streets. Furthermore, the park and its border streets were modeled as random variables that were finally classified according to the amount of PM2.5 concentration levels they carry. This classification was performed by using a method based on both Friedman’s test and the categories of the index of air quality of Quito. The results of this article showed that air pollution levels because of PM2.5 concentrations in La Carolina Park are not in alert level. The worst case, considering the analysis tools used in this article, is that one of the streets that border the park is in caution level. The other streets and parts of the park that were analyzed are either in a desirable level or in an acceptable level. Furthermore, in this article, it has been shown that as pedestrian and temporary residents move further away from the trees and vegetation of the park, the level of exposure to PM2.5 concentrations that they experience is higher. [ABSTRACT FROM AUTHOR]

Linear parametric neurotransmitter PET (lp-ntPET) is a novel kinetic model that estimates the temporal characteristics of a transient neurotransmitter component in PET data. To preserve computational simplicity in estimation, the parameters of the nonlinear term that describe this transient signal are discretized, and only a limited set of values for each parameter are allowed. Thus, linear estimation can be performed. Linear estimation is implemented using predefined basis functions that incorporate the discretized parameters. The implementation of the model using discretized parameters poses unique challenges for significance testing. Significance testing employs model comparison metrics to determine the significance of the improvement of the fit accomplished by including a basis function, i.e. it determines the presence of a transient signal in the PET data. A false positive occurs when the bases overfit data that do not contain a transient component. The number of parameters in a model, p, is necessary to determine the degrees of freedom in the model. In turn, p is crucial for the calculation of model selection metrics and controlling the false positive rate (FPR). In this work, we first explore the effect of parameter discretization on FPR by fitting simulated null data with varying numbers of bases. We demonstrate the dependence of FPR on number of bases. Then, we propose a correction to the number of parameters in the model, ${p}^{{\textit {eff}}}$ , which adapts to the number of bases used. Implementing model selection with ${p}^{{\textit {eff}}}$ maintains a stable FPR independent of number of bases. [ABSTRACT FROM AUTHOR]

Informally testing the fit of a probability distribution model is educationally a desirable precursor to formal methods for senior secondary school students. Limited research on how to teach such an informal approach, lack of statistically sound criteria to enable drawing of conclusions, as well as New Zealand assessment requirements led to this study. Focusing on the Poisson distribution, the criteria used by ten Grade 12 teachers for informally testing the fit of a probability distribution model was investigated using an online task-based interview procedure. It was found that criteria currently used by the teachers were unreliable as they could not correctly assess model fit, in particular, sample size was not taken into account. The teachers then used an interactive goodness of fit simulation-based visual inference tool (GFVIT) developed by the first author to determine if the teachers developed any new understandings about goodness of fit. After using GFVIT teachers reported a deeper understanding of model fit and that the tool had allowed them to take into account sample size when testing the fit of the probability distribution model through the visualization of expected distributional shape variation. Hence, a new informal test for the fit of a probability distribution is proposed. [ABSTRACT FROM AUTHOR]

Diameter and height are crucial parameters in forest inventories to determine the volume that is stored in the forest. The objective of this research was to generate an equation for eight federative entities that allows an accurate estimate of the timber volume of Abies religiosa in the center and south of the country. Around 2,747 trees were used to adjust equations of total tree roll volume, branch volume and total tree volume (vrta, vramas and vta). The following criteria were set for the selection of the best model; adjusted coefficient of determination, bias, mean error; as well as the graphical and numerical analysis of the residuals. Due to the lack of information on the branches, for Tlaxcala and Veracruz states only the total tree roll volume was obtained. The goodness of fit generated by the equations is reliable, since it explains more than 93% to the dependent variable, the errors are less than 0.47 m. These expressions are useful tools that can be applied by forestry technicians in different stands in the study area. [ABSTRACT FROM AUTHOR]

Importance of probability distribution functions in natural resource studies is increasing due to their effective roles in better understanding of vegetation structure and providing conceptual models of quantitative indices of plant species . The present study was performed to model the distribution of height and canopy area of Cionura erecta L. shrub, using probability distribution functions in Chahar-Tagh forest reserve in Chaharmahal and Bakhtiari Province. Height and crown cover (the largest and smallest diameters) of the studied species were measured by a strip meter in 35 sample plots of 10r area. The area of canopy cover was calculated by considering the crown shape of the studied species as a circle. Normal, Log-normal, Beta, Gamma, Weibull and Exponential probability distribution functions were used to model the height and canopy cover of the studied species and their goodness of fit were examined by Kolmogorov- Smirnov and Anderson Darling tests. Results showed bell-shaped distributions skewed to the right for height classes and in the case of the canopy cover it was decreasing. Beta and Gamma distribution functions were identified as the most appropriate functions for fitting to the height curve and Log-normal and Weibull functions were the most suitable ones for modeling the canopy cover. The present study showed that the quantitative characters of the studied species are far from a normal distribution under the influence of human activities. [ABSTRACT FROM AUTHOR]

The proper selection of statistical distributions is important for modeling port operations using simulations or queuing theory. The aim of this study was to determine the appropriate statistical distributions for modeling random processes related to ship operations in ports, including ship arrivals, berthing maneuver processes, service processes, and unberthing maneuver processes. A literature review was performed on the statistical distributions used in these random processes. In addition, the port data on ship operations gathered from three different ports in Turkey were examined. Goodness of fit tests were conducted to determine the appropriate distribution for each process. [ABSTRACT FROM AUTHOR]

Background: The 11th revision of the International Classification of Diseases and Related Disorders (ICD-11) has been released. In order to test the clinical consistency and the clinical utility of the proposed guidelines the World Health Organization (WHO) has carried out the Ecological Implementation Field Studies in various countries. In this paper the results of the Italian field trials on the clinical utility of the ICD-11 diagnostic guideline concerning schizophrenia and related disorders will be presented. Methods: In Italy, field trials have been carried out at the Department of Psychiatry of the University of Campania "L. Vanvitelli". All patients showing any psychotic symptom and referring to the outpatient and inpatient units have been recruited. Patients were interviewed by two clinicians with whom they had not had any prior clinical contact. At the end of each interview, clinicians were asked to complete 12 questions about the clinical utility of the diagnostic guidelines as applied to each patient. Results: Fourteen clinicians and 100 patients have been involved. The ICD-11 clinical guidelines were perceived as easy to use, with an adequate goodness of fit, clear and understandable and with an adequate level of details and specificity to describe the essential features of the diagnoses. Clinicians rated very positively their usefulness in describing the threshold between patient's disorder and normality. Despite still very positive, the guidelines have been perceived as less useful to select a treatment, to assess patients' prognosis and to communicate with other mental health professionals. Conclusions: The 11th revision of the chapter on Mental, Behavioural and Neurodevelopmental Disorders has made substantive changes to the conceptualization of mental disorders which could have impacted on their reliability and clinical utility. Results of the Italian field studies, in line with those reported by the international sample, highlight that ICD-11 has been rated as highly clinically useful by participating clinician, more than the ICD-10. This could be considered a good reason to be optimistic about the implementation of the ICD-11 among global clinicians. Trial registration The study has been approved by the Ethical Review Board of the University of Campania "L. Vanvitelli" (N. 416, 2016) [ABSTRACT FROM AUTHOR]

The coefficient of determination R2 and Pearson correlation coefficient ρ = R are standard metrics in hydrology for the evaluation of the goodness of fit between model simulations and observations, and as measures of the degree of dependence of one variable upon another. We show that the standard product moment estimator of ρ, termed r, while well-behaved for bivariate normal data, is upward biased and highly variable for bivariate non-normal data. We introduce three alternative estimators of ρ which are nearly unbiased and exhibit much less variability than r for non-normal data. We also document remarkable upward bias and tremendous increases in variability associated with r using both synthetic data and daily streamflow simulations from 905 calibrated rainfall–runoff models. We show that estimators of ρ = R accounting for skewness are needed for daily streamflow series because they exhibit high variability and skewness compared to, for example, monthly/annual series, where r should perform well. [ABSTRACT FROM AUTHOR]

In comprehending flood model results, we performed sensitivity analyses and evaluated how different combinations of digital elevation model (DEM) resolution and Manning's roughness affect flood maps produced from a 2D hydraulic model. Moreover, we analysed how the estimation of accuracy can further be influenced by the performance measure and the area's topography. Various combinations of DEM and Manning's n produced different results, in terms of quantified performance in relation to actual flood extent and the generated flood boundaries. High-resolution DEMs performed better with higher Manning's n , while lower n values were better for lower resolution DEMs. Furthermore, although lower resolution DEMs (25 and 50 m) received higher quantified performances, there are more discrepancies in the flood maps and water surface elevations (WSE) produced by them. The current statistical estimators of model performance do not necessarily provide an accurate estimate of which combination of DEM resolution and roughness are more suitable for application to modelling. Different statistical estimates have different assumptions, which can affect the model selection. Therefore, a more holistic approach towards model selection should be adopted that gives equal importance to statistical estimators, as well as the quality of flood inundation extents. [ABSTRACT FROM AUTHOR]

Approximation of Non-central Chi-square distribution as an empirical distribution of loglikelihood ratio test statistics (-2logλ; abbreviated as LRT) has been a concern in the field of structural equation modeling. Under extremely severe misspecification (Chun & Shapiro, 2009) reported that non-central Chi-square is not a good choice. In this paper, we have used a bootstrap sampling procedure to investigate the empirical null distribution of LRT specifically in the context of a latent class model (LCM) via frequentist framework (that is, EM algorithm). We used two types of data sets. The first type includes those sets of data on which LCM had been carried out (published results; named as "training data"). The other type is that of those data sets which are not published earlier (i.e. "real" collected data; named as "test data"). Non-central χ² distribution with degrees of freedom equals to the expected value of bootstrap LRT and non-centrality parameter equals to inverse of the variance of bootstrapped LRT is found to be very well fitted empirical null distribution of LRT in case of LCM. These results will help in obtaining the significance value of LRT for deciding on the number of classes present in a latent variable. [ABSTRACT FROM AUTHOR]

In standard item response theory (IRT) applications, the latent variable is typically assumed to be normally distributed. If the normality assumption is violated, the item parameter estimates can become biased. Summed score likelihood–based statistics may be useful for testing latent variable distribution fit. We develop Satorra–Bentler type moment adjustments to approximate the test statistics’ tail-area probability. A simulation study was conducted to examine the calibration and power of the unadjusted and adjusted statistics in various simulation conditions. Results show that the proposed indices have tail-area probabilities that can be closely approximated by central chi-squared random variables under the null hypothesis. Furthermore, the test statistics are focused. They are powerful for detecting latent variable distributional assumption violations, and not sensitive (correctly) to other forms of model misspecification such as multidimensionality. As a comparison, the goodness-of-fit statistic M2 has considerably lower power against latent variable nonnormality than the proposed indices. Empirical data from a patient-reported health outcomes study are used as illustration. [ABSTRACT FROM AUTHOR]

Background We believe errors in the risk assessment of acutely ill patients occur because only vital signs without concurrent functional capacity are considered. We, therefore, developed the PARIS risk score based on blood pressure, age, respiratory rate, loss of independence and oxygen saturation. Aim Validation of the PARIS score in four independent cohorts from three countries. Methods Retrospective cohort study of acutely ill patients admitted to hospitals in Denmark, Ireland and Uganda. Vital signs and functional capacity (registered as ability to stand or walk or get into bed unaided) was recorded upon arrival. Patients were followed up for 7 days (Denmark and Ireland) or until discharge (Uganda) and mortality recorded. The discriminatory power (ability to identify patients at increased risk) was determined using area under the receiver operating characteristics curve (AUROC) and calibration (precision) using Hosmer–Lemeshow goodness of fit test. Results Out of 14 447 patients, 327 (2.3%) died within 7 days: median age was 59 (39–75) years and 7458 (51.8%) were female. Seven-day mortality increased from 0.3% with a score of 0–26.7% with a score of 5. The score's AUROC as 0.833 [95% confidence interval (95% CI) 0.811–0.856], 0.817 (95% CI 0.792–0.842) and 0.894 (95% CI 0.813–0.974) for all patients, medical patients and surgical patients, respectively. However, except for surgical patients, calibration of the score was poor. Conclusion The PARIS score can identify both high and low risk acutely admitted medical and surgical patients, but calibration was poor for medical patients. [ABSTRACT FROM AUTHOR]

Optical signal propagation through underwater channels is affected by three main degrading phenomena, namely, absorption, scattering, and fading. In this paper, we experimentally study the statistical distribution of intensity fluctuations in underwater wireless optical channels with random temperature and salinity variations, as well as the presence of air bubbles. In particular, we define different scenarios to produce random fluctuations on the water refractive index across the propagation path and, then, examine the accuracy of various statistical distributions in terms of their goodness of fit to the experimental data. We also obtain the channel coherence time to address the average period of fading temporal variations. The scenarios under consideration cover a wide range of scintillation index from weak to strong turbulence. Moreover, the effects of beam-expander-and-collimator (BEC) at the transmitter side and aperture averaging lens (AAL) at the receiver side are experimentally investigated. We show that the use of a transmitter BEC and/or a receiver AAL suits single-lobe distributions, such that the generalized Gamma and exponentiated Weibull distributions can excellently match the histograms of the acquired data. Our experimental results further reveal that the channel coherence time is on the order of 10−3 s and larger which implies to the slow fading turbulent channels. [ABSTRACT FROM AUTHOR]

This paper proposes to incorporate goodness-of-fit (GoF) metrics as outputs—in addition to the synchronized phasor (or synchrophasor)—from a phasor measurement unit (PMU) to assess the performance quality of synchrophasor-based real-time applications, with specific focus on the accuracy of fault location along a transmission line. Typically, a PMU outputs quantities that describe the phasor-of-best-fit of a time-domain voltage or current signal. While a phasor accurately represents the actual measured signal in sinusoidal steady state, this may not be the case during electrical transients that occur immediately after sudden events, such as a fault. Unaware of this, the real-time application may not locate the fault accurately. By quantifying the accuracy of the phasor as compared with the actual time-domain signal to which the phasor is fit, GoF metrics help to assess the credibility of fault-location results. This hypothesis is verified via extensive case studies, and GoF-based criteria for sufficiently accurate fault-location results are uncovered. [ABSTRACT FROM PUBLISHER]

Ordinal outcomes are common in scientific research and everyday practice, and we often rely on regression models to make inference. A long-standing problem with such regression analyses is the lack of effective diagnostic tools for validating model assumptions. The difficulty arises from the fact that an ordinal variable has discrete values that are labeled with, but not, numerical values. The values merely represent ordered categories. In this article, we propose a surrogate approach to defining residuals for an ordinal outcome Y. The idea is to define a continuous variable S as a “surrogate” of Y and then obtain residuals based on S. For the general class of cumulative link regression models, we study the residual’s theoretical and graphical properties. We show that the residual has null properties similar to those of the common residuals for continuous outcomes. Our numerical studies demonstrate that the residual has power to detect misspecification with respect to (1) mean structures; (2) link functions; (3) heteroscedasticity; (4) proportionality; and (5) mixed populations. The proposed residual also enables us to develop numeric measures for goodness of fit using classical distance notions. Our results suggest that compared to a previously defined residual, our residual can reveal deeper insights into model diagnostics. We stress that this work focuses on residual analysis, rather than hypothesis testing. The latter has limited utility as it only provides a single p-value, whereas our residual can reveal what components of the model are misspecified and advise how to make improvements. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Experimental and simulation uncertainties have not been included in many of the statistics used in assessing agricultural model performance. The objectives of this study were to develop an F-test that can be used to evaluate model performance considering experimental and simulation uncertainties, and identify the best datasets to use for model calibration using different water stress functions in a cropping system model. Data on irrigated maize in Colorado, USA, and the Root Zone Water Quality Model (RZWQM) were used as an example to demonstrate model calibration using the modified F-test along with other commonly used statistics. Compared to the d-index, the F-test provided a statistical test under a certain confidence level that better distinguished the goodness of model prediction for both biomass and yield while considering uncertainty. To obtain robust model parameters, we recommend using multiple treatments across multiple years for model calibration, regardless of water stress functions used. [ABSTRACT FROM AUTHOR]

Monitoring animal populations is central to wildlife and fisheries management, and the use of N-mixture models toward these efforts has markedly increased in recent years. Nevertheless, relatively little work has evaluated estimator performance when basic assumptions are violated. Moreover, diagnostics to identify when bias in parameter estimates from N-mixture models is likely is largely unexplored. We simulated count data sets using 837 combinations of detection probability, number of sample units, number of survey occasions, and type and extent of heterogeneity in abundance or detectability. We fit Poisson N-mixture models to these data, quantified the bias associated with each combination, and evaluated if the parametric bootstrap goodness-of-fit (GOF) test can be used to indicate bias in parameter estimates. We also explored if assumption violations can be diagnosed prior to fitting N-mixture models. In doing so, we propose a new model diagnostic, which we term the quasi-coefficient of variation (QCV). N-mixture models performed well when assumptions were met and detection probabilities were moderate (i.e., ≥0.3), and the performance of the estimator improved with increasing survey occasions and sample units. However, the magnitude of bias in estimated mean abundance with even slight amounts of unmodeled heterogeneity was substantial. The parametric bootstrap GOF test did not perform well as a diagnostic for bias in parameter estimates when detectability and sample sizes were low. The results indicate the QCV is useful to diagnose potential bias and that potential bias associated with unidirectional trends in abundance or detectability can be diagnosed using Poisson regression. This study represents the most thorough assessment to date of assumption violations and diagnostics when fitting N-mixture models using the most commonly implemented error distribution. Unbiased estimates of population state variables are needed to properly inform management decision making. Therefore, we also discuss alternative approaches to yield unbiased estimates of population state variables using similar data types, and we stress that there is no substitute for an effective sample design that is grounded upon well-defined management objectives. [ABSTRACT FROM AUTHOR]

Professionals of the social and environmental sciences must solve problems (answer questions) based on data sampling and analyses. Commonly, all professionals face similar challenges: they need to take decisions on a population (e.g., all the trees of a region), but only have data from a sample (some trees of that region). A key tool in this process is to propose population models for the response variable (tree growth as a function of tree age and climatic conditions) and then use model predictions to take decisions (e.g., when to cut trees according to climatic conditions). In this paper we discuss how to propose, estimate, and select models of a population based on sampling data. We put special emphasis in proposing several alternative models (hypotheses) to solve one problem (e.g., different tree growth functions for age), which must be proposed before data sampling, including a null model (tree growth does not depend on tree age or climatic conditions). Models guide us on how data must be sampled for a valid contrast (growth measurements in trees of different age and under contrasting climates). Then, the Akaike information criterion (AIC) can be employed to sort the most parsimonious models, selecting those with the best goodness of fit (likelihood) and the lowest number of parameters (model complexity). Along the text, we introduce basic notions of multimodel inference and discuss common user mistakes. We provide real examples, and share their data and the analyses code in R, a free and open source software. In addition to be useful to professionals from different sciences, we expect our paper to promote the teaching of multimodel inference in graduate courses. [ABSTRACT FROM AUTHOR]

Fitting of lactation curves is a common tool to obtain the entire milk yield as well as to estimate the main curve characteristic (such as day of peak milk yield) for a lactation. These models are primarily designed for dairy cattle, but have been applied to nondairy cattle breeds and also for other species. In this study we considered milk yield data of 197 F2 crossbred cows of Charolais and German Holstein (founder breeds) for the first and the beginning of the second lactation. The F2 cows showed a high variability regarding the length of lactation, which varied between 7 and 406 d in milk for the first lactation. Thus, the data also show high variation regarding the daily and overall milk yield. To obtain complete lactation curves, we evaluated the lactation models of Ali-Schaeffer and Wilmink. To compare the 2 lactation models, we evaluated the goodness of fit using 6 evaluation criteria. The results show that the model of Ali-Schaeffer performs better on these highly inhomogeneous data, in contrast to the model of Wilmink. We discuss our findings from a statistical point of view and present possible biological reasons for the high variability regarding milk yield within the F2 population. Hence our findings may be helpful when milk yield data of crosses between dairy and beef cows (dual purpose) are investigated, whose lactation curves may not show the typical characteristics of dairy cattle. [ABSTRACT FROM AUTHOR]

With the expansion of advanced metering and increased use of energy analytics tools, the energy efficiency community has begun to explore the application of advanced measurement and verification (or ‘M&V 2.0′) technologies. Current literature recognizes their promise, but does not offer in-depth assessment of technical underpinnings. This paper assesses the state of the technology and its application. Sixteen commercially available technologies were characterized and combined with a national review of their use. [ABSTRACT FROM AUTHOR]

It is posited that the process of measuring the various parameters that characterize a signal is equivalent to a fitting problem in mathematics. The equation being fit is a model based on the “physics” of the signal. The Fourier transform or rms calculations in a phasor measurement unit (PMU) furnish the values of the coefficients. Regardless of exactly how the measurement is made, a metric we define and call the goodness of fit allows the measuring system to comment on the match between the signal it is observing and the model. The metric is based on the residuals, the differences between the signal itself and the value calculated from the result of measurement. Results from real-word PMUs and real-world signals illustrate that the equation of the PMU is well solved during steady conditions. We examine the effect of a fault in the transmission system on the goodness-of-fit metric for a PMU. We also apply the metric to results from a microPMU in the distribution system. [ABSTRACT FROM AUTHOR]

Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects exist or whether they are empirically meaningful. Hence, raising conclusions from the outcomes of statistical analyses is subject to limitations. NHST has been criticized for its misuse and the misconstruction of its outcomes, also stressing its inability to meet expectations that it was never designed to fulfil. Ironically, alternatives to NHST are identical in these respects, something that has been overlooked in their presentation. Three of those alternatives are discussed here (estimation via confidence intervals and effect sizes, quantification of evidence via Bayes factors, and mere reporting of descriptive statistics). None of them offers a solution to the problems that NHST is purported to have, all of them are susceptible to misuse and misinterpretation, and some bring around their own problems (e.g., Bayes factors have a one-to-one correspondence with p values, but they are entirely deprived of an inferential framework). Those alternatives also fail to cover a broad area of inference not involving distributional parameters, where NHST procedures remain the only (and suitable) option. Like knives or axes, NHST is not inherently evil; only misuse and misinterpretation of its outcomes needs to be eradicated. [ABSTRACT FROM AUTHOR]

This paper fits the three-parameter log-logistic (3LL) distribution to sulphur dioxide (SO2) monthly emissions in kilograms per gigawatt hour (kg/GWh) and in milligrams per cubic nano metre (mg/Nm3), at 13 of Eskom's coal fired power-generating stations in South Africa. The aim is to quantify and describe the emission of sulphur dioxide at these stations using a statistical distribution, and to also estimate the probabilities of extreme emissions and exceedances (emissions above a certain threshold). Using the 3LL distribution is proposed as such a distribution. The log-logistic distribution is a special form of a Burrtype distribution. Various goodness-of-fit measures, including the Kolmogorov Smirnov, the Anderson Darling and some graphical tests, are employed to test if the 3LL distribution is a good fit to the data. The maximum likelihood method is used to estimate the parameters. The distribution fit is important as it then becomes possible to quantify and manage the SO2 emissions effectively. The 3LL distribution, which is compared with three other distributions, gave the best overall fit to most of the power stations. [ABSTRACT FROM AUTHOR]

Usually, the exact time at which an event occurs cannot be observed for several reasons; for instance, it is not possible to constantly monitor a characteristic of interest. This generates a phenomenon known as censoring that can be classified as having a left censor, right censor or interval censor. When one is working with survival data in the presence of arbitrary censoring, the survival time of interest is defined as the elapsed time between an initial event and the next event that is generally unknown. This problem has been widely studied in the statistic literature and some progress has been made, toward resolving and the formulation of a bivariate likelihood to estimate parameters in a parametric regression model offers positive development opportunities. In this paper, we construct a bivariate likelihood for the Weibull regression model in the presence of interval censoring. Finally, its performance is illustrated by means of a simulation study. [ABSTRACT FROM AUTHOR]

We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial differential equations for the Fisher-Bingham distribution. [ABSTRACT FROM AUTHOR]

A three-parameters continuous distribution, namely, Power Lomax distribution (POLO) is proposed and studied for remission times of bladder cancer data. POLO distribution accommodate both inverted bathtub and decreasing hazard rate. Several statistical and reliability properties are derived. Point estimation via method of moments and maximum likelihood and the interval estimation are also studied. The simulation schemes are calculated to examine the bias and mean square error of the maximum likelihood parameter estimators. Finally, a real data application about the remission time of bladder cancer is used to illustrate the usefulness of the proposed distribution in modelling real data application. The characteristics of the fitting data using the proposed distribution are compared with known extensions of Lomax distribution. The comparison showed that the POLO distribution outfit most well-known extensions of Lomax distribution. [ABSTRACT FROM AUTHOR]

The size and shape of plant leaves change with growth, and an accurate description of leaf shape is crucial for describing plant morphogenesis and development. Bilateral symmetry, which has been widely observed but poorly examined, occurs in both dicot and monocot leaves, including all nominated bamboo species (approximately 1,300 species), of which at least 500 are found in China. Although there are apparent differences in leaf size among bamboo species due to genetic and environmental profiles, bamboo leaves have bilateral symmetry with parallel venation and appear similar across species. Here, we investigate whether the shape of bamboo leaves can be accurately described by a simplified Gielis equation, which consists of only two parameters (leaf length and shape) and produces a perfect bilateral shape. To test the applicability of this equation and the occurrence of bilateral symmetry, we first measured the leaf length of 42 bamboo species, examining >500 leaves per species. We then scanned 30 leaves per species that had approximately the same length as the median leaf length for that species. The leaf-shape data from scanned profiles were fitted to the simplified Gielis equation. Results confirmed that the equation fits the leaf-shape data extremely well, with the coefficients of determination being 0.995 on average. We further demonstrated the bilateral symmetry of bamboo leaves, with a clearly defined leaf-shape parameter of all 42 bamboo species investigated ranging from 0.02 to 0.1. This results in a simple and reliable tool for precise determination of bamboo species, with applications in forestry, ecology, and taxonomy. [ABSTRACT FROM AUTHOR]

A clear understanding of processes at multiple scales and levels is of special significance when conceiving strategies for human-environment interactions. However, understanding and application of the scale concept often differ between administrative-political and ecological disciplines. These mirror major differences in potential solutions whether and how scales can, at all, be made congruent. As a result, opportunities of seeking 'goodness-of-fit' between different concepts of governance should perhaps be reconsidered in the light of a potential 'generality of mis-fit.' This article reviews the interdisciplinary considerations inherent in the concept of scale in its ecological, as well as administrative-political, significance and argues that issues of how to manage 'mis-fit' should be awarded more emphasis in social-ecological research and management practices. These considerations are exemplified by the case of reindeer husbandry in Fennoscandia. Whilst an indigenous small-scale practice, reindeer husbandry involves multi-level ecological and administrative-political complexities-complexities that we argue may arise in any multi-level system. [ABSTRACT FROM AUTHOR]

This paper concentrates on a formal procedure for testing the goodness of fit of underlying theoretical probability distribution and evaluation of reliability indices for complicated systems like power generators. It is assumed that the repair times of these systems follow an exponential failure model with probability distribution function F (x). In view of the assessing goodness of it for the underlying distribution, directly on the repair hours, we find large chi-squire values and hence is not a good fit. To avoid this situation, a new procedure is introduced by using simulation technique. Failures are divided into two types of failures based on the repair time duration namely, (1) minor repairs and (2) major repairs based on a threshold value T.. A binomial probability model is considered for above two types of failures and carried out Chi-square test for goodness of it for the collected data. Based on the chi-square values, determined the Ideal threshold value which has smallest chi-square calculated value. Based on these identified ideal threshold value, reliabilities were calculated for each unit. Finally, reliability indices are calculated and presented graphically for the units under consideration and conclusions were drawn based on the results obtained. [ABSTRACT FROM AUTHOR]

The rootogram is a graphical tool associated with the work of J.W. Tukey that was originally used for assessing goodness of fit of univariate distributions. Here, we extend the rootogram to regression models and show that this is particularly useful for diagnosing and treating issues such as overdispersion and/or excess zeros in count data models. We also introduce a weighted version of the rootogram that can be applied out of sample or to (weighted) subsets of the data, for example, in finitemixture models. An empirical illustration revisiting a well-known dataset from ethology is included, for which a negative binomial hurdle model is employed. Supplementary materials providing two further illustrations are available online: the first, using data from public health, employs a two-component finite mixture of negative binomial models; the second, using data from finance, involves underdispersion. An R implementation of our tools is available in the R package countreg. It also contains the data and replication code. [ABSTRACT FROM AUTHOR]