Search Results (36)

This paper investigates the estimation of the stress–strength reliability parameter $\rho =P(X\le Y)$, where stress (X) and strength $\left(Y\right)$ are independently modeled by geometric distributions. Objective Bayesian approaches are employed by developing Jeffreys, reference, and probability-matching priors for $\rho$, and their effects on the resulting Bayes estimates are examined. Posterior inference is carried out using the random-walk Metropolis–Hastings algorithm. The performance of the proposed Bayesian estimators is assessed through extensive Monte Carlo simulations based on average estimates, root mean squared errors, and frequentist coverage probabilities of the highest posterior density credible intervals. Furthermore, the applicability of the methodology is demonstrated using two real data sets. Full article

Background: Atherosclerosis is a leading cause of cardiovascular morbidity and mortality worldwide. Although lipid-derived atherogenic indices are widely used for cardiovascular risk assessment, their relationship with sociodemographic factors, lifestyle behaviors, and health-related quality of life (HRQoL) in occupational populations remains insufficiently explored. This study aimed to evaluate the association between atherogenic risk, measured by total cholesterol/high-density lipoprotein cholesterol (TC/HDL-c), low-density lipoprotein cholesterol/high-density lipoprotein cholesterol (LDL-c/HDL-c), triglyceride/high-density lipoprotein cholesterol (TG/HDL-c), and atherogenic dyslipidemia (AD) and sociodemographic, lifestyle, and HRQoL variables in a large cohort of Spanish workers. Methods: We conducted a cross-sectional analysis of 100,014 Spanish workers aged 18–69 years, of whom 39.9% were women, with a mean age of 38.2 years (SD 10.2 or IQR) and 38.9 years (SD 10.3 or IQR) for men, during the health examinations carried out between 2021 and 2024. Sociodemographic variables included sex, age group, and occupational social class. Lifestyle factors comprised smoking status, adherence to the Mediterranean diet (MEDAS score), and physical activity (IPAQ categories). HRQoL was assessed using the 12-item Short Form Survey (SF-12), stratified into good vs. poor categories. Logistic regression models were applied to estimate odds ratios (OR) and 95% confidence intervals (CI) for moderate-to-high atherogenic risk across indices, adjusting for potential confounders. Results: Men exhibited a lower likelihood of moderate-to-high TC/HDL-c and LDL-c/HDL-c but a markedly higher probability of elevated TG/HDL-c and AD compared to women (OR range: 0.42–3.67, p < 0.001). A clear age-related gradient was observed across all indices, with participants aged 60–69 showing the highest risk (OR range: 2.28–7.84, p < 0.001). Lower social class, smoking, physical inactivity, poor diet, and poor SF-12 scores were significantly associated with increased atherogenic risk, with physical inactivity (OR up to 8.61) and poor diet (OR up to 4.98) emerging as the strongest predictors. Conclusions: Atherogenic risk in this large working cohort is strongly influenced by both traditional cardiovascular risk factors and HRQoL. Integrating lifestyle modification and quality-of-life improvement strategies into workplace health programs could substantially reduce the atherogenic burden. Longitudinal research is needed to confirm these associations and guide targeted interventions. Full article

The Maxwell–Boltzmann (MB) distribution is fundamental in statistical physics, providing an exact description of particle speed or energy distributions. In this study, a discrete formulation derived via the survival function discretization technique extends the MB model’s theoretical strengths to realistically handle lifetime and reliability data recorded in integer form, enabling accurate modeling under inherently discrete or censored observation schemes. The proposed discrete MB (DMB) model preserves the continuous MB’s flexibility in capturing diverse hazard rate shapes, while directly addressing the discrete and often censored nature of real-world lifetime and reliability data. Its formulation accommodates right-skewed, left-skewed, and symmetric probability mass functions with an inherently increasing hazard rate, enabling robust modeling of negatively skewed and monotonic-failure processes where competing discrete models underperform. We establish a comprehensive suite of distributional properties, including closed-form expressions for the probability mass, cumulative distribution, hazard functions, quantiles, raw moments, dispersion indices, and order statistics. For parameter estimation under Type-II censoring, we develop maximum likelihood, Bayesian, and bootstrap-based approaches and propose six distinct interval estimation methods encompassing frequentist, resampling, and Bayesian paradigms. Extensive Monte Carlo simulations systematically compare estimator performance across varying sample sizes, censoring levels, and prior structures, revealing the superiority of Bayesian–MCMC estimators with highest posterior density intervals in small- to moderate-sample regimes. Two genuine datasets—spanning engineering reliability and clinical survival contexts—demonstrate the DMB model’s superior goodness-of-fit and predictive accuracy over eleven competing discrete lifetime models. Full article

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. Full article

Background/Objectives: The rise in multidrug-resistant pathogens complicates UTI management, particularly in empirical therapy. This study aimed to develop and describe a Bayesian hierarchical weighted-incidence syndromic combination antibiogram (WISCA) model to optimize antibiotic selection for adult patients with community-onset UTIs. Methods: A retrospective study was conducted using a Bayesian hierarchical model. Data from microbiology laboratory records and medical databases were analyzed, focusing on age, prior antibiotic exposure, and clinical characteristics. Clinical outcomes, including extended hospital stays and in-hospital mortality, were evaluated before WISCA model development. Unlike traditional antibiograms, a WISCA integrates patient-specific factors to improve antimicrobial coverage estimations. A total of 11 monotherapies and 18 combination therapies were tested against 15 pathogens, with posterior coverage probabilities and 95% highest density intervals (HDIs) used to assess coverage. Results: Inappropriate final antibiotic treatment was associated with worse outcomes. The Bayesian framework improved estimations, particularly for rare pathogen–antibiotic interactions, increasing model applicability in high-resistance settings. Combination regimens showed superior coverage, especially in MDR cases and older adults. Conclusions: This study employed a comprehensive methodological approach for WISCA development, enhancing empirical antibiotic selection by incorporating local resistance data and patient-specific factors in a middle-income Latin American country with a high antimicrobial resistance profile. These findings provide a foundation for future clinical applications and antimicrobial stewardship strategies in high-resistance environments. Full article

The Birnbaum–Saunders (BS) distribution, defined only for non-negative values, is asymmetrical. However, it can be transformed into a normal distribution, which is symmetric. The BS distribution is particularly useful for analyzing data consisting of values greater than zero. This study aims to introduce six approaches for constructing confidence intervals for the difference and ratio of percentiles in Birnbaum–Saunders distributions containing zero values. The proposed approaches include the generalized confidence interval (GCI) approach, the bootstrap approach, the highest posterior density (HPD) approach based on the bootstrap method, the Bayesian approach, the HPD approach based on the Bayesian method, and the method of variance estimates recovery (MOVER) approach. To assess their performance, a Monte Carlo simulation study is conducted, focusing on coverage probability and average length. The results indicate that the MOVER approach and the HPD approach based on the Bayesian method perform better than other approaches for constructing confidence intervals for the difference between percentiles. Moreover, the GCI and Bayesian approaches outperform others when constructing confidence intervals for the ratio of percentiles. Finally, daily wind speed data from the Rayong and Prachin Buri provinces are used to demonstrate the efficacy of the proposed approaches. Full article

This paper investigates statistical methods for estimating unknown lifetime parameters using a progressive first-failure censoring dataset. The failure mode’s lifetime distribution is modeled by the odd-generalized-exponential–inverse-Weibull distribution. Maximum-likelihood estimators for the model parameters, including the survival, hazard, and inverse hazard rate functions, are obtained, though they lack closed-form expressions. The Newton–Raphson method is used to compute these estimations. Confidence intervals for the parameters are approximated via the normal distribution of the maximum-likelihood estimation. The Fisher information matrix is derived using the missing information principle, and the delta method is applied to approximate the confidence intervals for the survival, hazard rate, and inverse hazard rate functions. Bayes estimators were calculated with the squared error, linear exponential, and general entropy loss functions, utilizing independent gamma distributions for informative priors. Markov-chain Monte Carlo sampling provides the highest-posterior-density credible intervals and Bayesian point estimates for the parameters and reliability characteristics. This study evaluates these methods through Monte Carlo simulations, comparing Bayes and maximum-likelihood estimates based on mean squared errors for point estimates, average interval widths, and coverage probabilities for interval estimators. A real dataset is also analyzed to illustrate the proposed methods. Full article

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. Full article

The inverse Gaussian distribution is a two-parameter continuous probability distribution with positive support, which is used to account for the asymmetry of the positively skewed data that are often seen when modeling environmental phenomena, such as $P{M}_{2.5}$ levels. The coefficient of variation is often used to assess variability within datasets, and the common coefficient of variation of several independent samples can be used to draw inferences between them. Herein, we provide estimation methods for the confidence interval for the common coefficient of variation of multiple inverse Gaussian distributions by using the generalized confidence interval (GCI), the fiducial confidence interval (FCI), the adjusted method of variance estimates recovery (MOVER), and the Bayesian credible interval (BCI) and highest posterior density (HPD) methods using the Jeffreys prior rule. The estimation methods were evaluated based on their coverage probabilities and average lengths, using a Monte Carlo simulation study. The findings indicate the superiority of the GCI over the other methods for nearly all of the scenarios considered. This was confirmed for a real-world scenario involving $P{M}_{2.5}$ data from three provinces in northeastern Thailand that followed inverse Gaussian distributions. Full article

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples. Full article

This study investigated the effect of a commercially available ketone supplement on heart rate (HR), perceived exertion (RPE), blood lactate, glucose, and ketone concentrations, along with time to fatigue (TTF) during a running task to voluntary fatigue. Twelve NCAA Division I cross-country athletes took part in this randomized, double-blind, placebo-controlled cross-over study. Bayesian methodologies were employed for all statistical analyses, and point estimates were determined to be statistically significant if the 95% highest-density intervals (HDI) excluded zero. TTF was not significantly different between conditions with a Mean_diff = 48.7 ± 6.3 s (95% HDI: −335, 424) and a 0.39 probability derived from the posterior distribution, indicating the likelihood that the supplement would increase TTF compared to the placebo control. Lactate concentrations immediately post-exercise were significantly lower in the supplement trial relative to placebo with an estimated Mean_diff = −4.6 ± 1.9 mmol; 95% HDI: −8.3, −0.9. There were no significant interaction effects observed for either blood glucose or ketone concentrations nor HR or RPE. These findings imply that the acute ingestion of ketones before running at lactate threshold pace has a low probability of increasing TTF in highly trained Division I runners. Full article

Due to slash/burn agricultural activity and frequent forest fires, $P{M}_{2.5}$ has become a significant air pollution problem in Thailand, especially in the north and north east regions. Since its dispersion differs both spatially and temporally, estimating $P{M}_{2.5}$ concentrations discretely by area, for which the inverse Gaussian distribution is suitable, can provide valuable information. Herein, we provide derivations of the simultaneous confidence interval for the ratios of the coefficients of variation of multiple inverse Gaussian distributions using the generalized confidence interval, the Bayesian interval based on the Jeffreys’ rule prior, the fiducial interval, and the method of variance estimates recovery. The efficacies of these methods were compared by considering the coverage probability and average length obtained from simulation results of daily $P{M}_{2.5}$ datasets. The findings indicate that in most instances, the fiducial method with the highest posterior density demonstrated a superior performance. However, in certain scenarios, the Bayesian approach using the Jeffreys’ rule prior for the highest posterior density yielded favorable results. Full article

The unit log-logistic distribution is a suitable choice for modeling data enclosed within the unit interval. In this paper, estimating the parameters of the unit-log-logistic distribution is performed through a Bayesian approach with non-informative priors. Specifically, we use Jeffreys, reference, and matching priors, with the latter depending on the interest parameter. We derive the corresponding posterior distributions and validate their propriety. The Bayes estimators are then computed using Markov Chain Monte Carlo techniques. To assess the finite sample performance of these Bayes estimators, we conduct Monte Carlo simulations, evaluating their mean squared errors and their coverage probabilities of the highest posterior density credible intervals. Finally, we use these priors to obtain estimations and credible sets for the parameters in an example of a real data set for illustrative purposes. Full article

The Weibull distribution is a continuous probability distribution that finds wide application in various fields for analyzing real-world data. Specifically, wind speed data often adhere to the Weibull distribution. In our study, our aim is to compare the mean wind speed datasets from different areas in Thailand. To achieve this, we proposed simultaneous confidence intervals for all pairwise differences between the means of Weibull distributions. The generalized confidence interval (GCI), method of variance estimates recovery (MOVER), and a Bayesian approach, utilizing both gamma and uniform prior distributions, are proposed to construct simultaneous confidence intervals. Through simulations, we find that the Bayesian highest posterior density (HPD) interval using a gamma prior distribution demonstrates satisfactory performance, while the GCI proves to be a viable alternative. Finally, we applied these proposed approaches to real wind speed data in northeastern and southern Thailand to illustrate their effectiveness and practicality. Full article

Today, the reliability or quality practitioner always aims to shorten testing duration and reduce testing costs without neglecting efficient statistical inference. So, a generalized progressively Type-II hybrid censored mechanism has been developed in which the experimenter prepays for usage of the testing facility for T units of time. This paper investigates the issue of estimating the model parameter, reliability, and hazard rate functions of the Maxwell–Boltzmann distribution in the presence of generalized progressive Type-II hybrid censored data by making use of the likelihood and Bayesian inferential methods. Using an inverse gamma prior distribution, the Bayes estimators of the same unknown parameters with respect to the most commonly squared-error loss are derived. Since the joint likelihood function is produced in complex form, following the Monte-Carlo Markov-chain idea, the Bayes’ point estimators as well as the Bayes credible and highest posterior density intervals cannot be derived analytically, but they may be examined numerically. Via the normal approximation of the acquired maximum likelihood and log-maximum-likelihood estimators, the approximate confidence interval bounds of the unknown quantities are derived. Via comprehensive numerical comparisons, with regard to simulated root mean squared-error, mean relative absolute bias, average confidence length, and coverage probability, the actual behavior of the proposed estimation methodologies is examined. To illustrate how the offered methodologies may be used in real circumstances, two different applications, representing the failure time points of aircraft windscreens as well as the daily average wind speed in Cairo during 2009, are explored. Numerical evaluations recommend utilizing a Bayes model via the Metropolis-Hastings technique to produce samples from the posterior distribution to estimate any parameter of the Maxwell–Boltzmann distribution when collecting data from a generalized progressively Type-II hybrid censored mechanism. Full article