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Purpose The purpose of this paper is to estimate the multicomponent reliability by assuming the unit-Gompertz (UG) distribution. Both stress and strength are assumed to have an UG distribution with common scale parameter. Design/methodology/approach The reliability of a multicomponent stress–strength system is obtained by the maximum likelihood (MLE) and Bayesian method of estimation. Bayes estimates of system reliability are obtained by using Lindley’s approximation and Metropolis–Hastings (M–H) algorithm methods when all the parameters are unknown. The highest posterior density credible interval is obtained by using M–H algorithm method. Besides, uniformly minimum variance unbiased estimator and exact Bayes estimates of system reliability have been obtained when the common scale parameter is known and the results are compared for both small and large samples. Findings Based on the simulation results, the authors observe that Bayes method provides better estimation results as compared to MLE. Proposed asymptotic and HPD intervals show satisfactory coverage probabilities. However, average length of HPD intervals tends to remain shorter than the corresponding asymptotic interval. Overall the authors have observed that better estimates of the reliability may be achieved when the common scale parameter is known. Originality/value Most of the lifetime distributions used in reliability analysis, such as exponential, Lindley, gamma, lognormal, Weibull and Chen, only exhibit constant, monotonically increasing, decreasing and bathtub-shaped hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rates are upside-down bathtub and bathtub-shaped, which are found in the unit-Gompertz distribution. Furthermore, when reliability is measured as percentage or ratio, it is important to have models defined on the unit interval in order to have plausible results. Therefore, the authors have studied the multicomponent stress–strength reliability under the unit-Gompertz distribution by comparing the MLEs, Bayes estimators and UMVUEs.

PurposeThe purpose of this article is to derive inference for multicomponent reliability where stress-strength variables follow unit generalized Rayleigh (GR) distributions with common scale parameter.Design/methodology/approachThe authors derive inference for the unknown parametric function using classical and Bayesian approaches. In sequel, (weighted) least square (LS) and maximum product of spacing methods are used to estimate the reliability. Bootstrapping is also considered for this purpose. Bayesian inference is derived under gamma prior distributions. In consequence credible intervals are constructed. For the known common scale, unbiased estimator is obtained and is compared with the corresponding exact Bayes estimate.FindingsDifferent point and interval estimators of the reliability are examined using Monte Carlo simulations for different sample sizes. In summary, the authors observe that Bayes estimators obtained using gamma prior distributions perform well compared to the other studied estimators. The average length (AL) of highest posterior density (HPD) interval remains shorter than other proposed intervals. Further coverage probabilities of all the intervals are reasonably satisfactory. A data analysis is also presented in support of studied estimation methods. It is noted that proposed methods work good for the considered estimation problem.Originality/valueIn the literature various probability distributions which are often analyzed in life test studies are mostly unbounded in nature, that is, their support of positive probabilities lie in infinite interval. This class of distributions includes generalized exponential, Burr family, gamma, lognormal and Weibull models, among others. In many situations the authors need to analyze data which lie in bounded interval like average height of individual, survival time from a disease, income per-capita etc. Thus use of probability models with support on finite intervals becomes inevitable. The authors have investigated stress-strength reliability based on unit GR distribution. Useful comments are obtained based on the numerical study.

Understanding the distribution of communication disabilities is crucial for effective policy planning and resource allocation. This study introduces the Extended Generalized Inverted Kumaraswamy Standard Exponential ( EGIKwS -Exp) distribution for modeling the percentage of Saudi individuals with severe or total communication disabilities aged two years and above across 13 administrative regions. The dataset, sourced from Disability Statistics 2023, exhibits significant variability, requiring a flexible probabilistic framework. The EGIKwS -Exp distribution, an extension of the exponential model, enhances adaptability for complex datasets like disability statistics. Key distributional and reliability properties, including hazard rate, reversed hazard rate, c umulative hazard, and survival functions, are derived. Parameter estimation is conducted using Maximum Likelihood Estimation, with Bayesian inference via MCMC Metropolis-Hastings, Asymptotic, Boot-P, Boot-T, and Highest Posterior Density confidence intervals ensuring robust analysis. Graphical reliability measures confirm the model’s efficiency in capturing trends in communication disability data, offering a comprehensive framework for analyzing regional disparities and informing policymakers. By providing a robust statistical tool, this research supports more informed decision-making in disability studies and public health planning.

This article proposes methodology for assessing goodness of fit in Bayesian hierarchical models. The methodology is based on comparing values of pivotal discrepancy measures (PDMs), computed using parameter values drawn from the posterior distribution, to known reference distributions. Because the resulting diagnostics can be calculated from standard output of Markov chain Monte Carlo algorithms, their computational costs are minimal. Several simulation studies are provided, each of which suggests that diagnostics based on PDMs have higher statistical power than comparable posterior‐predictive diagnostic checks in detecting model departures. The proposed methodology is illustrated in a clinical application; an application to discrete data is described in supplementary material.

Accurate characterization of sexual dimorphism is crucial in evolutionary biology because of its significance in understanding present and past adaptations involving reproductive and resource use strategies of species. However, inferring dimorphism in fossil assemblages is difficult, particularly with relatively low dimorphism. Commonly used methods of estimating dimorphism levels in fossils include the mean method, the binomial dimorphism index, and the coefficient of variation method. These methods have been reported to overestimate low levels of dimorphism, which is problematic when investigating issues such as canine size dimorphism in primates and its relation to reproductive strategies. Here, we introduce the posterior density peak (pdPeak) method that utilizes the Bayesian inference to provide posterior probability densities of dimorphism levels and within-sex variance. The highest posterior density point is termed the pdPeak. We investigated performance of the pdPeak method and made comparisons with the above-mentioned conventional methods via 1) computer-generated samples simulating a range of conditions and 2) application to canine crown-diameter datasets of extant known-sex anthropoids. Results showed that the pdPeak method is capable of unbiased estimates in a broader range of dimorphism levels than the other methods and uniquely provides reliable interval estimates. Although attention is required to its underestimation tendency when some of the distributional assumptions are violated, we demonstrate that the pdPeak method enables a more accurate dimorphism estimate at lower dimorphism levels than previously possible, which is important to illuminating human evolution.

The inverse Gaussian distribution is characterized by its asymmetry and right-skewed shape, indicating a longer tail on the right side. This distribution represents extreme values in one direction, such as waiting times, stochastic processes, and accident counts. Moreover, depending on if the accident counts data can occur or not and may have zero value, the Delta Inverse Gaussian (Delta-IG) distribution is more suitable. The confidence interval (CI) for the coefficient of variation (CV) of the Delta-IG distribution in accident counts is essential for risk assessment, resource allocation, and the creation of transportation safety policies. Our objective is to establish CIs of CV for the Delta-IG population using various methods. We considered seven CI construction methods, namely Generalized Confidence Interval (GCI), Adjusted Generalized Confidence Interval (AGCI), Parametric Bootstrap Percentile Confidence Interval (PBPCI), Fiducial Confidence Interval (FCI), Fiducial Highest Posterior Density Confidence Interval (F-HPDCI), Bayesian Credible Interval (BCI), and Bayesian Highest Posterior Density Credible Interval (B-HPDCI). We utilized Monte Carlo simulations to assess the proposed CI technique for average widths (AWs) and coverage probability (CP). Our findings revealed that F-HPDCI and AGCI exhibited the most effective coverage probability and average widths. We applied these methods to generate CIs of CV for accident counts in India.

The Rayleigh distribution is a continuous probability distribution that is inherently asymmetric and commonly used to model right-skewed data. It holds significant importance across a wide range of scientific and engineering disciplines and exhibits structural relationships with several other asymmetric probability distributions, for example, Weibull and exponential distribution. This research proposes techniques for establishing credible intervals and confidence intervals for the single mean of the zero-inflated two-parameter Rayleigh distribution. The study introduces methods such as the percentile bootstrap, generalized confidence interval, standard confidence interval, approximate normal using the delta method, Bayesian credible interval, and Bayesian highest posterior density. The effectiveness of the proposed methods is assessed by evaluating coverage probability and expected length through Monte Carlo simulations. The results indicate that the Bayesian highest posterior density method outperforms the other approaches. Finally, the study applies the proposed methods to construct confidence intervals for the single mean using real-world data on COVID-19 total deaths in Singapore during October 2022.

Human Immunodeficiency Virus (HIV) remains a significant public health challenge, particularly in low-resource settings, where limited knowledge contributes to its spread, especially among women facing socio-economic and educational barriers. This study examines the associations between misconceptions about HIV transmission and sociodemographic factors among Somali women. Identifying regions and groups with limited awareness will help prioritize targeted education and healthcare interventions, aligning with the National Strategic Plan (NSP). A multivariable Bayesian logistic regression model was used to analyze data from the 2018-2019 Somali Demographic and Health Survey (SDHS). This modeling approach was chosen for its ability to handle uncertainty and incorporate prior knowledge into the analysis. Bayesian adjusted odds ratios (BAORs) with 95% highest posterior density intervals (HPDIs) were calculated to determine significant associations between misconceptions and sociodemographic factors. The study found that 67.18% of women had misconceptions about HIV transmission. Significant factors associated with misconceptions included age, education, wealth, and internet usage. Women aged 30-34 (BAOR = 0.94, 95% HPDI: 0.90-0.98), 35-39 (BAOR = 0.94, 95% HPDI: 0.90-0.98), and 40-44 (BAOR = 0.93, 95% HPDI: 0.89-0.98), women with secondary education (BAOR = 0.92, 95% HPDI: 0.88-0.95), women with higher education (BAOR = 0.84, 95% HPDI: 0.79-0.88), women in the highest wealth quintile (BAOR = 0.90, 95% HPDI: 0.86-0.95), and women who had never used the internet (BAOR = 1.06, 95% HPDI: 1.03-1.09). This study highlights the critical need for targeted interventions to reduce misconceptions about HIV transmission among Somali women. Policies should focus on educating younger women, promoting female education, implementing region-specific health interventions, and enhancing internet access and digital literacy, particularly in rural areas, to improve HIV knowledge and support public health efforts.

This study addresses the estimation of the common mean for the zero-inflated inverse Gaussian (ZIIG) distributions, a problem not previously explored. The performance of four interval estimation approaches was evaluated: the generalized confidence interval (GCI), parametric bootstrap, Bayesian, and highest posterior density (HPD). Simulation studies under varying sample sizes, zero-inflation probabilities, mean values, and shape parameters revealed notable differences in coverage probability (CP) and average length (AL). For small samples, the GCI and parametric bootstrap approaches often under-covered, particularly in highly skewed or heavily zero-inflated cases. In contrast, Bayesian and HPD intervals generally maintained coverage closer to the nominal 0.95 level, albeit with longer intervals. As sample size increased, all methods approached nominal coverage and produced shorter intervals, improving precision. Overall, the Bayesian and HPD approaches demonstrated strong robustness across conditions, with HPD intervals frequently achieving accurate coverage with shorter lengths. Finally, the proposed approaches were applied to real-world data on road accident fatalities in Thailand.

Simon's two-stage design is one of the most commonly used methods in phase II clinical trials with binary endpoints. The design tests the null hypothesis that the response rate is less than an uninteresting level, versus the alternative hypothesis that the response rate is greater than a desirable target level. From a Bayesian perspective, we compute the posterior probabilities of the null and alternative hypotheses given that a promising result is declared in Simon's design. Our study reveals that because the frequentist hypothesis testing framework places its focus on the null hypothesis, a potentially efficacious treatment identified by rejecting the null under Simon's design could have only less than 10% posterior probability of attaining the desirable target level. Due to the indifference region between the null and alternative, rejecting the null does not necessarily mean that the drug achieves the desirable response level. To clarify such ambiguity, we propose a Bayesian enhancement two-stage (BET) design, which guarantees a high posterior probability of the response rate reaching the target level, while allowing for early termination and sample size saving in case that the drug's response rate is smaller than the clinically uninteresting level. Moreover, the BET design can be naturally adapted to accommodate survival endpoints. We conduct extensive simulation studies to examine the empirical performance of our design and present two trial examples as applications.