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This work focusses on extending the deep compartment model (DCM) framework to the estimation of mixed-effects. By introducing random effects, model predictions can be personalized based on drug measurements, enabling the testing of different treatment schedules on an individual basis. The performance of classical first-order (FO and FOCE) and machine learning based variational inference (VI) algorithms were compared in a simulation study. In VI, posterior distributions of the random variables are approximated using variational distributions whose parameters can be directly optimized. We found that variational approximations estimated using the path derivative gradient estimator version of VI were highly accurate. Models fit on the simulated data set using the FO and VI objective functions gave similar results, with accurate predictions of both the population parameters and covariate effects. Contrastingly, models fit using FOCE depicted erratic behaviour during optimization, and resulting parameter estimates were inaccurate. Finally, we compared the performance of the methods on two real-world data sets of haemophilia A patients who received standard half-life factor VIII concentrates during prophylactic and perioperative settings. Again, models fit using FO and VI depicted similar results, although some models fit using FO presented divergent results. Again, models fit using FOCE were unstable. In conclusion, we show that mixed-effects estimation using the DCM is feasible. VI performs conditional estimation, which might lead to more accurate results in more complex models compared to the FO method. [ABSTRACT FROM AUTHOR]

A three-parameter probability distribution is derived from a composed cumulative distribution function, which is itself a family of bounded support transformations. The transformed model called the doubly bounded exponential distribution, which exhibits decreasing shaped density while the hazard rate has increasing shape. Some statistical properties are obtained in closed form, such as the moments and various entropy functions. The parameter estimation is carried out by the methods of maximum likelihood estimate, least squares estimate, weighted least squares estimate, Anderson-Darling estimate, and Cramér-von Mises estimate. The performance of these estimators is assessed through a Monte Carlo simulation study. The identifiability of the DB-Exp model's parameters is also investigated. The proposed distribution can produce a higher performance than several well-known bounded distributions in the literature, as shown by an application to rainfall data. [ABSTRACT FROM AUTHOR]

A novel distribution family named the Transmuted Odd Moment Exponential-G (TOME-G) family is introduced, derived from both the Odd Moment Exponential-G and Transmuted families. Within this family, three distinct models are proposed: the transmuted odd moment exponential Lomax (TOMEL) distribution, transmuted odd moment exponential Rayleigh (TOMER) distribution, and transmuted odd moment exponential exponential (TOMEE) distribution. The density function shape for each model, such as symmetric or asymmetric (including right-skewed, left-skewed, increasing, decreasing, and uni-modal), is discussed. Key statistical characteristics of the family, including the expansion of the probability density function (PDF), moments, incomplete moment, Mo generating function, residual life, and reversed residual life functions, are derived. Additionally, three estimation methods—maximum likelihood estimation (MLE), Ordinary Least Squares Estimator (OLSE), and Weighted Least Squares Estimator (WLE)—are examined for estimating model parameters. A simulation study is conducted to compare the performance of these estimation methods. We covered two real-life applications in this study, both involving life tests. One of them is in the engineering domain, aiming to study the time to failure between manufactured units. The other application is in the medical field, focusing on leukemia data for life tests. [ABSTRACT FROM AUTHOR]

A novel distribution family named the Transmuted Odd Moment Exponential-G (TOME-G) family is introduced, derived from both the Odd Moment Exponential-G and Transmuted families. Within this family, three distinct models are proposed: the transmuted odd moment exponential Lomax (TOMEL) distribution, transmuted odd moment exponential Rayleigh (TOMER) distribution, and transmuted odd moment exponential exponential (TOMEE) distribution. The density function shape for each model, such as symmetric or asymmetric (including right-skewed, left-skewed, increasing, decreasing, and uni-modal), is discussed. Key statistical characteristics of the family, including the expansion of the probability density function (PDF), moments, incomplete moment, Mo generating function, residual life, and reversed residual life functions, are derived. Additionally, three estimation methods—maximum likelihood estimation (MLE), Ordinary Least Squares Estimator (OLSE), and Weighted Least Squares Estimator (WLE)—are examined for estimating model parameters. A simulation study is conducted to compare the performance of these estimation methods. We covered two real-life applications in this study, both involving life tests. One of them is in the engineering domain, aiming to study the time to failure between manufactured units. The other application is in the medical field, focusing on leukemia data for life tests.

Understanding direct and indirect relationships of environmental, socio-economic and climate variables and the dynamics of epidemics is key to guiding targeted public health policy and interventions. This study investigates the direct and indirect effects of environmental and socio-economic factors on the COVID-19 dynamics in Africa (54 African countries from 2019 to 2021) using SEM approach. Specifically, the study aimed to: (i) assess the performance of two SEM estimation methods (Lisrel and PLS-SEM) in relationship to sample size (100, 200, 500, and 1000) and level of model complexity (No, two, and four indirect effects) and (ii) use the most performing SEM estimation method to examine direct and indirect effects of factors influencing the number of cases and deaths of COVID-19 in Africa. The results highlight a positive spatial correlation between factors such as temperature, humidity, age, the proportion of people aged over 65, and the COVID-19 incidence. Under the control of confounding factors, Lisrel turns out to be the most performing method, identifying climate, demographic and economic factors as the main determinants of COVID-19 dynamics. These factors have a direct and significant impact on the incidence of COVID-19. An indirect relationship was also observed between economic factors and the incidence of COVID-19 through air pollutants. The results highlight the importance of considering these factors in understanding the spread of the virus to avoid further disasters.

Abstract This research introduces a novel two-parameter distribution, the power-modified XLindley distribution, developed through the application of power transformation techniques to the existing modified XLindley distribution. This new distribution enhances flexibility and adaptability in statistical modeling. We conduct a thorough examination of its statistical properties, exploring its potential to improve data fitting and modeling accuracy. To assess the effectiveness of the model, we employ multiple estimation techniques and evaluate their performance through extensive simulation experiments. Our findings indicate that the maximum product of the spacings method is particularly effective for parameter estimation. To demonstrate the practical utility of the proposed model, we apply it to two real-world datasets: one related to flood data and the other to reliability engineering. The results underscore the distribution’s superior ability to capture the characteristics of these datasets compared to existing models, highlighting its significance for applications in natural disaster analysis and reliability studies.

The mixed causal‐non‐causal invertible‐non‐invertible autoregressive moving‐average (MARMA) models have the advantage of incorporating roots inside the unit circle, thus adjusting the dynamics of financial returns that depend on future expectations. This article introduces new techniques for estimating, identifying and simulating MARMA models. Although the estimation of the parameters is done using second‐order moments, the identification relies on the existence of high‐order dynamics, captured in the high‐order spectral densities and the correlation of the squared residuals. A comprehensive Monte Carlo study demonstrated the robust performance of our estimation and identification methods. We propose an empirical application to 24 portfolios from emerging markets based on the factors: size, book‐to‐market, profitability, investment and momentum. All portfolios exhibited forward‐looking behavior, showing significant non‐causal and non‐invertible dynamics. Moreover, we found the residuals to be uncorrelated and independent, with no trace of conditional volatility. [ABSTRACT FROM AUTHOR]

The new continuous class of probability distribution named the Power Burr X-T (PBX-T) family is proposed in this paper. The essential characteristics of the PBX-T family of distributions, i.e. conventional moments and associated procedures, stress-strength reliability, and Rényi entropy, are derived and studied. Some special models belonging to the new family have been comprehensively explored concerning their shapes. Extensive simulations have been conducted to compare the maximum likelihood (ML) estimates with other classical estimators. It is found that the mean squared errors and the bias of the ML estimates are relatively least for large samples. Moreover, real-life applications from medical and engineering fields have been used to demonstrate the potentiality and adequacy of the suggested sub-models from the PBX-T family. The values of observed goodness-of-fit measures show that the sub-models of the suggested family of distributions are superior in adequacy parallel to the other generalized models. [ABSTRACT FROM AUTHOR]

This paper introduces a bounded probability distribution which is derived from the Muth distribution. The main statistical properties are studied and analytical expressions are provided for the moments, incomplete moments, inverse of the cumulative distribution function, extropy, Lorentz and Bonferroni curves, among others. Moreover, it possesses both monotone and non-monotone hazard rate functions so the new distribution is rich enough to model real data. Different estimation methods are applied to estimate the parameters of the model and a Monte Carlo simulation study assesses their performances. The usefulness in practical applications is illustrated using two real data sets and the results show that the proposed distribution provides better fits than other competing distributions commonly used to model data with bounded support. [ABSTRACT FROM AUTHOR]

In this review study, the major available methods for measurement and estimation of evapotranspiration (ET) are discussed briefly while explaining the latest developments. The best available validation methods are also reviewed and explained. It highlights the importance of accurate ET quantification in managing water resources, evaluating climate change impacts, and supporting crop water requirement management. Measurement methods such as scintillometry, lysimetry, and the eddy covariance (EC) flux method are presented. Additionally, hydrological models are discussed as estimation approaches for actual and potential ET. The paper explores various ET estimation products, particularly those based on remote sensing techniques. Specifically, methods like Mapping EvapoTranspiration at high Resolution with Internalized Calibration (METRIC), Simplified Surface Energy Balance Operational (SSEBop ET), Moderate Resolution Imaging Spectroradiometer (MOD16), Surface Energy Balance Algorithm for Land (SEBAL), Global Land Surface Evaporation: Amsterdam Methodology (GLEAM), Satellite Application Facility on Land Surface Analysis (LSA‐SAF), and Global Land Data Assimilation System (GLDAS) are described. The integration of machine learning (ML) with EC and remote sensing is investigated, with a comprehensive discussion of different ML approaches. Validation methods including the EC method, water balance method‐derived ET (WBET), and statistical techniques are explained. Overall, this review paper provides a comprehensive overview of ET quantification, covering measurement techniques, estimation approaches, remote sensing methods, and the integration of ML. The insights gained from this review contribute to a profound knowledge of ET dynamics and helps those sectors dealing with drought monitoring, water resource management and climate change assessments. [ABSTRACT FROM AUTHOR]

Understanding direct and indirect relationships of environmental, socio-economic and climate variables and the dynamics of epidemics is key to guiding targeted public health policy and interventions. This study investigates the direct and indirect effects of environmental and socio-economic factors on the COVID-19 dynamics in Africa (54 African countries from 2019 to 2021) using SEM approach. Specifically, the study aimed to: (i) assess the performance of two SEM estimation methods (Lisrel and PLS-SEM) in relationship to sample size (100, 200, 500, and 1000) and level of model complexity (No, two, and four indirect effects) and (ii) use the most performing SEM estimation method to examine direct and indirect effects of factors influencing the number of cases and deaths of COVID-19 in Africa. The results highlight a positive spatial correlation between factors such as temperature, humidity, age, the proportion of people aged over 65, and the COVID-19 incidence. Under the control of confounding factors, Lisrel turns out to be the most performing method, identifying climate, demographic and economic factors as the main determinants of COVID-19 dynamics. These factors have a direct and significant impact on the incidence of COVID-19. An indirect relationship was also observed between economic factors and the incidence of COVID-19 through air pollutants. The results highlight the importance of considering these factors in understanding the spread of the virus to avoid further disasters. [ABSTRACT FROM AUTHOR]

van Raalte et al. (2023) alerted demographers to the potential dangers of calculating cohort measures from the "diagonals" of gridded age–period (AP) data. In the case of cohort fertility, however, a minor change to the estimation procedure can mitigate the trend and cohort size biases that the authors identify. With an appropriate algorithm, researchers can estimate cohort fertility indices from AP data quite well. [ABSTRACT FROM AUTHOR]

The proposed article introduces a novel three-parameter lifetime model called an exponentiated extended extreme-value (EEEV) distribution model. The EEEV distribution is characterized by increasing or bathtub-shaped hazard rates, which can be advantageous in the context of reliability. Various statistical properties of the distribution have been derived. The article discusses four estimation methods, namely, maximum likelihood, least squares, weighted least squares, and Cramer-von Mises, for EEEV distribution parameter estimation. A simulation study was carried out ´ to examine the performance of the new model estimators based on the four estimation methods by using the average bias, mean squared errors, relative absolute biases, and root mean square error. The flexibility and significance of the EEEV distribution are demonstrated by analyzing three real-world datasets from the fields of medicine and engineering. The EEEV distribution exhibits high adaptability and outperforms several well-known statistical models in terms of performance. [ABSTRACT FROM AUTHOR]

The proposed article introduces a novel three-parameter lifetime model called an exponentiated extended extreme-value (EEEV) distribution model. The EEEV distribution is characterized by increasing or bathtub-shaped hazard rates, which can be advantageous in the context of reliability. Various statistical properties of the distribution have been derived. The article discusses four estimation methods, namely, maximum likelihood, least squares, weighted least squares, and Cramér-von Mises, for EEEV distribution parameter estimation. A simulation study was carried out to examine the performance of the new model estimators based on the four estimation methods by using the average bias, mean squared errors, relative absolute biases, and root mean square error. The flexibility and significance of the EEEV distribution are demonstrated by analyzing three real-world datasets from the fields of medicine and engineering. The EEEV distribution exhibits high adaptability and outperforms several well-known statistical models in terms of performance.

In this study, we introduce the modified Burr III Odds Ratio–G distribution, a novel statistical model that integrates the odds ratio concept with the foundational Burr III distribution. The spotlight of our investigation is cast on a key subclass within this innovative framework, designated as the Burr III Scaled Inverse Odds Ratio–G (B-SIOR-G) distribution. By effectively integrating the odds ratio with the Burr III distribution, this model enhances both flexibility and predictive accuracy. We delve into a thorough exploration of this distribution family's mathematical and statistical properties, spanning hazard rate functions, quantile functions, moments, and additional features. Through rigorous simulation, we affirm the robustness of the B-SIOR-G model. The flexibility and practicality of the B-SIOR-G model are demonstrated through its application to four datasets, highlighting its enhanced efficacy over several well-established distributions. [ABSTRACT FROM AUTHOR]

Mazucheli et al. (J Appl Stat 46(4):700–714, 2019) introduced unit Lindley distribution by transforming Lindley (J Roy Stat Soc Ser B Stat Methodol 20(1):102–107, 1958) distribution for modelling proportion data. In this paper, we consider an exponential version of unit Lindley distribution. Various statistical and structural properties of the new distribution are discussed such as moments, hazard rate function, inequality measures, entropy etc. Different estimation methods are used to estimate the parameters of the model and their performances are demonstrated by Monte Carlo simulation. Finally the dominance of proposed distribution is embellished through real life data sets by comparing with some other unit distributions available in literature. [ABSTRACT FROM AUTHOR]

The intertwining relationship between sustainability and discrete probability distributions found its significance in decision-making processes and risk assessment frameworks. Count data modeling and its practical applications have gained attention in numerous research studies. This investigation focused on a particular discrete distribution characterized by a single parameter obtained through the survival discretization method. Statistical attributes of this distribution were accurately explicated using generalized hypergeometric functions. The unveiled characteristics highlighted its suitability for analyzing data displaying "right-skewed" asymmetry and possessing extended "heavy" tails. Its failure rate function effectively addressed scenarios marked by a consistent decrease in rates. Furthermore, it proved to be a valuable tool for probabilistic modeling of over-dispersed data. The study introduced various estimation methods such as maximum product of spacings, Anderson-Darling, right-tail Anderson-Darling, maximum likelihood, least-squares, weighted least-squares, percentile, and Cramer-Von-Mises, offering comprehensive explanations. A ranking simulation study was conducted to evaluate the performance of these estimators, employing ranking techniques to identify the most effective estimator across different sample sizes. Finally, real-world sustainability engineering and medical datasets were analyzed to demonstrate the significance and application of the newly introduced model. [ABSTRACT FROM AUTHOR]

The intertwining relationship between sustainability and discrete probability distributions found its significance in decision-making processes and risk assessment frameworks. Count data modeling and its practical applications have gained attention in numerous research studies. This investigation focused on a particular discrete distribution characterized by a single parameter obtained through the survival discretization method. Statistical attributes of this distribution were accurately explicated using generalized hypergeometric functions. The unveiled characteristics highlighted its suitability for analyzing data displaying "right-skewed" asymmetry and possessing extended "heavy" tails. Its failure rate function effectively addressed scenarios marked by a consistent decrease in rates. Furthermore, it proved to be a valuable tool for probabilistic modeling of over-dispersed data. The study introduced various estimation methods such as maximum product of spacings, Anderson-Darling, right-tail Anderson-Darling, maximum likelihood, least-squares, weighted least-squares, percentile, and Cramer-Von-Mises, offering comprehensive explanations. A ranking simulation study was conducted to evaluate the performance of these estimators, employing ranking techniques to identify the most effective estimator across different sample sizes. Finally, real-world sustainability engineering and medical datasets were analyzed to demonstrate the significance and application of the newly introduced model.

Abstract In the present study, we develop and investigate the odd Frechet Half-Logistic (OFHL) distribution that was developed by incorporating the half-logistic and odd Frechet-G family. The OFHL model has very adaptable probability functions: decreasing, increasing, bathtub and inverted U shapes are shown for the hazard rate functions, illustrating the model’s capacity for flexibility. A comprehensive account of the mathematical and statistical properties of the proposed model is presented. In estimation viewpoint, six distinct estimation methodologies are used to estimate the unknown parameters of the OFHL model. Furthermore, an extensive Monte Carlo simulation analysis is used to evaluate the effectiveness of these estimators. Finally, two applications to real data are used to demonstrate the versatility of the suggested method, and the comparison is made with the half-logistic and some of its well-known extensions. The actual implementation shows that the suggested model performs better than competing models.

Simulation studies are needed to investigate how many score categories are sufficient to treat ordered categorical data as continuous, particularly for bifactor models. The current simulation study aims to address such needs by investigating the performance of estimation methods in the bifactor models with ordered categorical data. Results support the application of categorical estimators to the ordered categorical data rather than the continuous estimators when sample size is large (750). Otherwise, an applied researcher may have to use the continuous estimators due to the model non-convergence. In this circumstance, the number of response categories needs to be at least 6 to avoid the rejection of correctly specified bifactor models by the chi-square test and estimate the model parameters accurately. The robust maximum likelihood (MLR) may be chosen among two continuous estimators due to its smaller type I error rate for the chi-square test than the ML. Practical implications of study findings are discussed. [ABSTRACT FROM AUTHOR]

In this study, we introduce a novel and robust approach for computing Generalizability Theory (GT) absolute error and related dependability indices using indicator intercepts that represent observed means within structural equation models (SEMs). We demonstrate the applicability of our method using one-, two-, and three-facet designs with self-report measures having varying numbers of scale points. Results for the indicator mean-based method align well with those obtained from the GENOVA and R gtheory packages for doing conventional GT analyses and improve upon previously suggested methods for deriving absolute error and corresponding dependability indices from SEMs when analyzing three-facet designs. We further extend our approach to derive Monte Carlo confidence intervals for all key indices and to incorporate estimation procedures that correct for scale coarseness effects commonly observed when analyzing binary or ordinal data. [ABSTRACT FROM AUTHOR]

There are examples in the literature demonstrating different approaches to defining the item characteristic functions (ICF) and characterizing the latent variable time-course within a pharmacometrics item response theory (IRT) framework. One such method estimates both the ICF and latent variable time-course simultaneously, and another method establishes the ICF first then models the latent variable directly. To date, a direct comparison of the “simultaneous” and “sequential” methodologies described in this work has not yet been systematically investigated. Item parameters from a graded response IRT model developed from Parkinson’s Progression Marker Initiative (PPMI) study data were used as simulation parameters. Each method was evaluated under the following conditions: (i) with and without drug effect and (ii) slow progression rate with smaller sample size and rapid progression rate with larger sample size. Overall, the methods performed similarly, with low bias and good precision for key parameters and hypothesis testing for drug effect. The ICF parameters were well determined when the model was correctly specified, with an increase in precision in the scenario with rapid progression. In terms of drug effect, both methods had large estimation bias for the slow progression rate; however, this bias can be considered small relative to overall progression rate. Both methods demonstrated type 1 error control and similar discrimination between model with and without drug effect. The simultaneous method was slightly more precise than the sequential method while the sequential method was more robust towards longitudinal model misspecification and offers practical advantages in model building. [ABSTRACT FROM AUTHOR]

We study the different properties of the Rayleigh distribution. These include the descriptive properties, reliability properties and stochastic orders. Next, we consider seven different estimation methods for estimating the parameter, namely: maximum likelihood estimation, matching moments estimation, maximum product of spacing estimation, ordinary least squares estimation, Cramér-von Mises estimation, Anderson-Darling estimation and right-tail Anderson-Darling estimation. A simulation study is done to assess the performance of these methods of estimation and the results shows that all the estimators are mostly efficient and consistent. Finally, using the method of maximum likelihood estimation, we demonstrate the applicability of the Rayleigh distribution by modelling the Netherlands’s COVID-19 mortality rate data as an example. [ABSTRACT FROM AUTHOR]

This study addresses the difficulties associated with parameter estimation in the generalized power unit half-logistic geometric distribution by employing a progressive Type-Ⅱ censoring technique. The study uses a variety of methods, including maximum likelihood, maximum product of spacing, and Bayesian estimation. The work investigates Bayesian estimators taking into account a gamma prior and a symmetric loss function while working with observed data produced by likelihood and spacing functions. A full simulation experiment is carried out with varying sample sizes and censoring mechanisms in order to thoroughly evaluate the various estimation approaches. The highest posterior density approach is employed in the study to compute credible intervals for the parameters. Additionally, based on three optimal criteria, the study chooses the best progressive censoring scheme from a variety of rival methods. The study examines two real datasets in order to confirm the applicability of the generalized power unit half-logistic geometric distribution and the efficacy of the suggested estimators. The results show that in order to generate the necessary estimators, the maximum product of the spacing approach is better than the maximum likelihood method. Furthermore, as compared to traditional methods, the Bayesian strategy that makes use of probability and spacing functions produces estimates that are more satisfactory.

The estimation of wind potential is generally assessed using the two parameters of Weibull distribution (k, c). Relative Percentage Error (RPE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Relative Root Mean Square Error (RRMSE), Correlation Coefficient (R), and Index of Agreement (IA) are calculated to comparatively analyze five numerical methods of computing Weibull parameters. The five selected methods are (Empirical Justus (EMJ), Energy Pattern Factor (EPFM), Maximum Likelihood (MLM), Method of Moment (MOM), and L-moment Estimation Method (L-MOM)). With the daily wind speed dataset for the year 2014 measured at 10 m height, the five methods have been applied on the study site Al-Hodeidah city in Yemen. Therefore, compared to other methods, the EPFM method is the most accurate method for estimating the Weibull parameters, while the L-MOM method is the least accurate at 10, 30, and 50 m heights. Moreover, this study reveals that the parameter remains the same with height, while the c parameter increases with height. The values of the skewness and kurtosis of wind speed and power density do not change as height changes.

The exponential distribution is one of the most widely used statistical distribution for reliability issues. In this paper, we introduce a novel family based on the exponential model, called the new exponential-H (NEx-H) family. The sub-models of the NEx-H family are capable of accommodating variable failure rates, as well as unimodal, bimodal, left-skewed, symmetric, right-skewed, and J-shape densities. The mathematical features of the NEx-H family are derived. The parameters of the NEx-Weibull distribution are estimated by using seven estimation methods. Detailed numerical simulations are presented. Based on our study, the maximum likelihood is the best estimation method for estimating the NEx-Weibull parameters. Three real-life data sets are fitted using the NEx-Weibull distribution. The NEx-Weibull model provides better fit as compared to some competing Weibull models.

The World Health Organization (WHO) announced on March 11, 2020, that COVID-19 could be considered a pandemic. This epidemic has become a huge issue for academics, doctors, healthcare providers, epidemiologists, and decision-makers alike. Motivated by studying natural phenomena, we concentrated on making a statistical model capable of fitting natural pandemics into the whole world. In this manuscript, we introduced a new novel distribution called the Inverse Power Haq (IPH) distribution. We created this distribution due to its formidable merits. We introduced its statistical properties and plotted its probability density function (PDF), cumulative distribution function (CDF), and hazard rate function (HRF). We utilized classical estimation techniques to determine the parameters for the suggested distribution. In the paper's conclusion, we performed a data analysis, applying the distribution to COVID-19 infection in Kuwait for practical purposes. Our analysis demonstrated the superior performance of the proposed distribution compared to its competitors, establishing it as the most suitable choice for modeling COVID-19 data in patients of different ages. Lastly, the conclusion section includes a summary of our overall findings and conclusions.

This paper introduces the q-analogues of the generalized extreme value distribution and its discrete counterpart under power normalization. The inclusion of the parameter q enhances modeling flexibility. The continuous extended model can produce various types of hazard rate functions, with supports that can be finite, infinite, or bounded above or below. Additionally, these new models can effectively handle skewed data, particularly those with highly extreme observations. Statistical properties of the proposed continuous distribution are presented, and the model parameters are estimated using various approaches. A simulation study evaluates the performance of the estimators across different sample sizes. Finally, three distinct real datasets are analyzed to demonstrate the versatility of the proposed model.

This study addresses the difficulties associated with parameter estimation in the generalized power unit half-logistic geometric distribution by employing a progressive Type-II censoring technique. The study uses a variety of methods, including maximum likelihood, maximum product of spacing, and Bayesian estimation. The work investigates Bayesian estimators taking into account a gamma prior and a symmetric loss function while working with observed data produced by likelihood and spacing functions. A full simulation experiment is carried out with varying sample sizes and censoring mechanisms in order to thoroughly evaluate the various estimation approaches. The highest posterior density approach is employed in the study to compute credible intervals for the parameters. Additionally, based on three optimal criteria, the study chooses the best progressive censoring scheme from a variety of rival methods. The study examines two real datasets in order to confirm the applicability of the generalized power unit half-logistic geometric distribution and the efficacy of the suggested estimators. The results show that in order to generate the necessary estimators, the maximum product of the spacing approach is better than the maximum likelihood method. Furthermore, as compared to traditional methods, the Bayesian strategy that makes use of probability and spacing functions produces estimates that are more satisfactory. [ABSTRACT FROM AUTHOR]

This article is an extension of the Chris-Jerry distribution (C-JD) in that a two-parameter Chris-Jerry distribution (TPCJD) is suggested and its characteristics are studied. Based on the determined domain of attraction and other major statistical properties, the proposed TPCJD seems to fit into the Gumbel domain. Additionally, it has been confirmed that the stress strength is reliable. The tail study suggests that the TPCJD's substantial tail makes it suited for a range of applications. The study took into account the single acceptance sampling approach using both simulation and real-life situations. The parameters of the TPCJD were estimated by some classical and Bayesian approaches. The mean squared errors (MSE), linear-exponential, and generalized entropy loss functions were deployed to obtain the Bayesian estimators aided by the Markov chain Monte Carlo (MCMC) simulation. An analysis of lifetime data on two events justified the use of the proposed distribution after comparing the results with some standard lifetime models. [ABSTRACT FROM AUTHOR]

Model estimates were made for changes in the actual evaporation of boreal forests in the taiga zone of European Russia caused by climate evolution in the XXI century. Climate changes were forecasted using the results of calculations by an MGO regional climate model. The space and time specification of the forecast data was made with the use of a model of the atmospheric boundary layer. Variations of the forecasted changes due to the use of different methods to calculate evaporation were studied. Calculations based on an additional (complementary) relationship, determining the actual evaporation with the use of standard meteorological characteristics were compared with observations and calculations based on a detail model of energy transport in a forest massif. The model values of the actual evaporation in the XXI century increase all over the European Russia. The effect of the intensity of dry periods on the evolution of actual evaporation is analyzed. It is shown that, despite the arid climate, the effect of dry periods on taiga forests will be moderately negative. [ABSTRACT FROM AUTHOR]

This paper introduces a new three-parameter distribution called the modified Kies Gompertz (MKGO) distribution to identify an effective statistical distribution in a real-life modeling data set. The distribution’s probability density function may take numerous forms and graphs, and it could be negatively and positively skewed and uni-modal. We established several statistical properties of the MKGO distribution, such as moments, skewness, kurtosis, moment generating function, distribution of order statistic, quantile function, stress strength reliability and two cases of entropy measures. Further, we proposed six methods for estimating the unknown parameters of the suggested model. A brief Monter Carlo (MC) simulation study is illustrated in terms of average estimate (AE) and mean square error (MSE). to show the efficiency of these estimators. Finally, we analyzed four real data sets in the engineering sector to evaluate the potential of the proposed model with that of various existing distributions.

In this study, we introduce the modified Burr III Odds Ratio–G distribution, a novel statistical model that integrates the odds ratio concept with the foundational Burr III distribution. The spotlight of our investigation is cast on a key subclass within this innovative framework, designated as the Burr III Scaled Inverse Odds Ratio–G (B-SIOR-G) distribution. By effectively integrating the odds ratio with the Burr III distribution, this model enhances both flexibility and predictive accuracy. We delve into a thorough exploration of this distribution family’s mathematical and statistical properties, spanning hazard rate functions, quantile functions, moments, and additional features. Through rigorous simulation, we affirm the robustness of the B-SIOR-G model. The flexibility and practicality of the B-SIOR-G model are demonstrated through its application to four datasets, highlighting its enhanced efficacy over several well-established distributions.

The compressive strength of normal-weight concrete can be well-described by the Weibull distribution, but there is a lack of research on the efficiency of the estimation methods employed for determining the Weibull distribution parameters. This study investigates the three common methods of estimating the parameters of the Weibull distribution, namely, linear regression, maximum likelihood, and moment methods. These methods are implemented on three datasets comprising a total of 490 compressive strength values of different concretes prepared using various mix proportions as well as varying sizes, shapes, and types of specimens. The effectiveness of the three estimation methods is evaluated based on the Anderson-Darling and Kolmogorov-Smirnov tests as well as the AIC and BIC approaches. The present performance analysis reveals that: (i) the maximum likelihood method shows the most accuracy, while the moments method exhibits the least relevance in estimating the Weibull distribution parameters; (ii) as an impact of the sample-size dependency of concrete compressive strength, the efficiency of the Weibull distribution and its parameters are influenced by the specimen size; (iii) the less dispersion in the dataset, the better the compatibility of the Weibull distribution of concrete compressive strength; and (iv) the Weibull modulus of concrete is linearly proportional to the inverse of the coefficient of variation of the measured strength data, with a proportionality coefficient of 1.09, regardless of the types and sizes of the concrete sample as well as mix proportions.

In this article, we extensively study a family of distributions using the trigonometric function. We add an extra parameter to the sine transformation family and name it the alpha-sine-G family of distributions. Some important functional forms and properties of the family are provided in a general form. A specific sub-model alpha-sine Weibull of this family is also introduced using the Weibull distribution as a parent distribution and studied deeply. The statistical properties of this new distribution are investigated and intended parameters are estimated using the maximum likelihood, maximum product of spacings, least square, weighted least square, and minimum distance methods. For further justification of these estimates, a simulation experiment is carried out. Two real data sets are analyzed to show the suggested model's application. The suggested model performed well compares to some existing models considered in the study. [ABSTRACT FROM AUTHOR]

Simple Summary: In this study, we perform a sensitivity analysis in similarity-based predictive models using computational simulations and two distinct methodologies, while focusing on a biological application. We utilize a linear regression model as a reference point. We gauge sensitivity by calculating the coefficient of variation of the parameter estimators from three different models. Our findings show that the first approach outperforms the second one when dealing with categorical variables. Moreover, this first approach offers the advantage of being more parsimonious due to a smaller number of parameters. Predictive models based on empirical similarity are instrumental in biology and data science, where the premise is to measure the likeness of one observation with others in the same dataset. Biological datasets often encompass data that can be categorized. When using empirical similarity-based predictive models, two strategies for handling categorical covariates exist. The first strategy retains categorical covariates in their original form, applying distance measures and allocating weights to each covariate. In contrast, the second strategy creates binary variables, representing each variable level independently, and computes similarity measures solely through the Euclidean distance. This study performs a sensitivity analysis of these two strategies using computational simulations, and applies the results to a biological context. We use a linear regression model as a reference point, and consider two methods for estimating the model parameters, alongside exponential and fractional inverse similarity functions. The sensitivity is evaluated by determining the coefficient of variation of the parameter estimators across the three models as a measure of relative variability. Our results suggest that the first strategy excels over the second one in effectively dealing with categorical variables, and offers greater parsimony due to the use of fewer parameters. [ABSTRACT FROM AUTHOR]

This paper introduces a flexible three-parameter extension of the Lomax model called the odd Lomax–Lomax (OLxLx) distribution. The OLxLx distribution can provide left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, constant, unimodal, and decreasing hazard rate shapes. Some mathematical properties of the introduced model are derived. The OLxLx density can be expressed as mixture of Lomax densities. The OLxLx parameters are estimated by using eight estimation methods and their performance is explored by using detailed simulation studies. The partial and overall ranks of the mean relative errors, absolute biases, and mean square errors of different estimators are presented to choose the best estimation method. The flexibility and applicability of the OLxLx distribution is shown using real-life medicine data, illustrating the superior fit of the OLxLx distribution over other competing Lomax distributions. The OLxLX distribution outperforms some rival Lomax distributions including the Kumaraswamy–Lomax, McDonald–Lomax, Weibull–Lomax, transmuted Weibull–Lomax, exponentiated-Lomax, Lomax–Weibull, modified Kies–Lomax, Burr X Lomax, beta exponentiated-Lomax, odd exponentiated half-logistic Lomax, and transmuted-Lomax distributions, among others. [ABSTRACT FROM AUTHOR]

In this manuscript we introduce a new distribution called the novel alpha power Fréchet(NAPF) distribution. We introduce its mathematical properties and its probability density function (PDF) and Cumulative distribution function (CDF) in a closed form. We made a simulation study to estimate the parameters of the proposed distribution. We made point estimation using six classical methods. We generated complete sample using the R software that used in the estimation process. We applied different real data sets on the proposed distribution to asses the performance of it against all its competitors. We used different type of data. We used the Kolimingrov Sminrov (KS) algorithm to make the goodness of fit test for the complete data. We estimated all information criteria and we deduced that the proposed distribution outperforms all its competitors, and we concluded that the proposed distribution is a very good candidate for modelling complete data. We studied the existence and uniqueness of the log-likelihood function which must be studied to make sure that the likelihood function provides maximum estimates for the parameters.

This work proposes a new two-parameter model, titled Topp-Leone (A) model. The main benefit of the new model is that it has an inverted bathtub shaped curve, increasing and decreasing hazard rate function quite dependent on the shape parameter. Its structural properties including the ordinary moments, quantiles, probability weighted moment, median, entropy and order statistics are derived. More so, the survival, failure rate, reversed failure rate and cumulative failure rate functions are also derived. Six classical estimation methods are discussed for estimating the parameters of the new model. Monte Carlo experiments and real datasets analyses are conducted to examine the classical estimators performance of this model. Finally, the usefulness of the Topp-Leone (A) model demonstrated with different applications to complete and type-II right censored data proves its more flexible when compared to well-known models in statistical literature. [ABSTRACT FROM AUTHOR]

This paper introduces a new three-parameter distribution called the modified Kies Gompertz (MKGO) distribution to identify an effective statistical distribution in a real-life modeling data set. The distribution's probability density function may take numerous forms and graphs, and it could be negatively and positively skewed and uni-modal. We established several statistical properties of the MKGO distribution, such as moments, skewness, kurtosis, moment generating function, distribution of order statistic, quantile function, stress strength reliability and two cases of entropy measures. Further, we proposed six methods for estimating the unknown parameters of the suggested model. A brief Monter Carlo (MC) simulation study is illustrated in terms of average estimate (AE) and mean square error (MSE). to show the efficiency of these estimators. Finally, we analyzed four real data sets in the engineering sector to evaluate the potential of the proposed model with that of various existing distributions. [ABSTRACT FROM AUTHOR]

Structural Equation Modeling (SEM) is used to analyze the causal relationships between observable and unobservable variables. Among the assumptions considered, but not essential, for the application of the SEM are the presence of multivariate normality between the data, and the need for a large number of observations, in order to obtain the variances and covariances between the variables. It is not always possible to have access to a sufficiently large number of observations to enable the calculation of parameters, and the convergence of the iterative algorithm is one of the problems in obtaining the results. This work investigates the convergence of iterative algorithms, which minimize the variation of parameters, through a stipulated convergence rate, using the Maximum Likelihood (ML) and Generalized Least Squares (GLS) estimation methods on structural equation models using confirmatory factor analysis (CFA) and regression models. Convergences were evaluated in relation to the number of observations, in order to obtain a minimum quantity sufficient for a convergence rate above 50%. The calculations were performed in the statistical environment R® version 3.4.4, and the results obtained showed a convergence rate above 50% for models estimated by GLS, even with the data showing lack of multivariate normality, kurtosis and accentuated asymmetry. Thus, it was possible to define a minimum number of observations necessary for an adequate convergence of the iterative algorithms in obtaining the necessary parameters. [ABSTRACT FROM AUTHOR]

Using the Monte Carlo simulation method, this study analyzes the impacts on fit indices by the degree of nonnormality of variables, the sample size, and the choice of estimation method. To address these issues, we use the causal model of consumer involvement as elaborated by Mittal and Lee. Results of this study show that adjusted goodness of fit index (AGFI) and goodness of fit index (GFI) are subject to variation in sample size, and their use requires a sample size of at least 300 observations to be reliable. Comparative fit index (CFI) and root mean square error of approximation (RSMEA) are more reliable with the generalized least squares (GLS) compared with maximum likelihood estimation (MLE) method under different settings of sample size and degree of nonnormality. Finally, for the standardized root mean square residual (SRMR), it is recommended that it is used with the MLE method. This study provides prescriptions for the choice of fit indices and the requirements of sample size and estimation method to test the causal model of consumer involvement. The method used here can be extended to any model before fitting it to real data. It helps researchers to prevent conflictual results regarding the choice of fit indices. [ABSTRACT FROM AUTHOR]