Abstract

Abstract

Chikungunya is a vector-borne viral disease caused by the mosquitoes  Aedes aegypti and  Aedes albopictus. There is no specific medical treatment or available vaccine. This work presents a host-vector model that considers two age structures: chronological age and asymptomatic infection age. This model accounts for variability in the relapse period and susceptibility to the chikungunya virus. From this system of integro-differential equations, a particular case is derived in the form of ordinary differential equations (ODEs). The objective of this study is to estimate the basic reproductive number R0 of the ODE model for a chikungunya outbreak that occurred in 2015 in Acapulco, Mexico. A Bayesian approach using Hamiltonian Monte Carlo methods is applied to estimate the parameters of the ODE model and subsequently estimate R0. We estimate that R0 is 2.61, with a 95% credibility interval of (1.66, 3.80), which is consistent with other reports in the literature.

Abstract

This paper aims to estimate the unknown parameters for the exponentiated Rayleigh distribution using Type-I hybrid censored data under a step-stress model. The maximum likelihood and Bayes methods estimate the parameters and acceleration factor. The parameters’ approximate confidence intervals are created. The Bayes estimates of the parameters for the squared error and linear exponential loss functions are computed using the Markov Chain Monte Carlo (MCMC) method. Finally, we perform a simulation study to evaluate the effectiveness of the proposed estimators. We provide a real-life data example (Strength data measurement in GPA, for single and impregnated carbon fibers) to explain the obtained results.OPEN ACCESS Received: 15/04/2025 Accepted: 21/08/2025 Published: 27/10/2025

Abstract

Many lifetime analysis, such as engineering, biology, survival, actuarial and medical sciences, heavily rely on the two-parameter compound Rayleigh exponential distribution, which is well-known in statistical theory. Because of their ability to successfully handle small sample sizes and involve prior knowledge, Bayesian techniques are crucial for estimating the parameters of the compound Rayleigh exponential distribution. This study presents the estimation of the compound Rayleigh exponential distribution unknown parameters using Bayesian and non-Bayesian estimation techniques, including maximum likelihood estimation, maximum product spacing, least square estimator, weighted least square estimator, Cramer-Von-Mise estimator, Anderson-Darling estimator, and Bayesian techniques with informative and non-informative priors based on different loss functions. Additionally, we used several methods to obtain the confidence intervals for the unknown parameters, such as the approximate and Bootstrap methods. The effectiveness of these estimators is evaluated through a Monte Carlo simulation study. Furthermore, we are committed to investigating three widely recognized risk metrics: the value at risk, the tail value at risk, and the tail variance premium. These findings are helpful for actuarial risk researchers who depend on risk measurement fitting when evaluating Bayesian tools for effectively modeling actuarial sciences. Finally, different applications taken from several areas are examined to illustrate the practical usefulness of the compound Rayleigh exponential distribution. Using various model selection criteria, the introduced model is contrasted with that of several well-known distributions. Our empirical findings indicate that the suggested model has superior goodness-of-fit to the other models examined.

Abstract

In reliability and lifetime studies, it is often impractical to observe the failure times of all units in a sample, particularly when the process is timeconsuming or expensive. Type II censoring addresses this by terminating the experiment after a predetermined number of failures from a total sample of size. The Discrete Alpha Power Extended Inverted Weibull distribution is particularly suitable for modeling such censored discrete lifetime data. Its flexible shape parameters allow it to capture a wide range of failure behaviors, including over-dispersion, which is common in censored datasets. In this context, the likelihood function and estimation procedures (maximum likelihood and Bayesian) explicitly account for the censoring, ensuring unbiased parameter estimates and reliable predictive inferences. Consequently, the Discrete Alpha Power Extended Inverted Weibull distribution provides a practical and statistically robust framework for analyzing discrete lifetimes under type II censoring.OPEN ACCESS Received: 28/07/2025 Accepted: 19/09/2025 Published: 23/01/2026

Abstract

Accelerated life testing has become essential in modern reliability assessment, particularly for high-reliability products where traditional testing is often impractical due to time constraints. This study introduces a comprehensive framework for reliability analysis using Weibull-based partially accelerated life tests under a unified hybrid censoring scheme. Assuming lifetimes follow a Weibull distribution, we provide both classical and Bayesian estimation procedures to estimate core quantities, shape, scale, and the acceleration factor, alongside reliability metrics at normal operating conditions. The inferential framework encompasses point estimation along with uncertainty quantification, using both approximate confidence intervals and Bayesian credible intervals derived from Markov Chain Monte Carlo methods. A comprehensive Monte Carlo simulation study evaluates the performance of various methods in terms of mean squared error, interval coverage, and average interval width across a range of censoring patterns. The results provide actionable insights and practical recommendations for selecting appropriate methods and designing future studies under different censoring scenarios. The proposed methodology is further illustrated through two real-world case studies: the reliability of white organic light-emitting diodes and the lifetime of micro-droplets in ambient environments. These examples highlight the method’s flexibility and practical relevance in both engineering and biomedical reliability applications.OPEN ACCESS Received: 31/07/2025 Accepted: 10/09/2025 Published: 23/01/2026

Abstract

A highly adaptable censoring framework, known as the unified TypeI progressive hybrid censoring scheme, has been recently introduced as an enhancement to the unified hybrid censoring approach. However, this censoring method has a significant limitation: it assumes that the removal pattern is fixed and established prior to conducting the experiment, which may lack practical applicability. This study presents, for the first time, the unified Type-I progressive hybrid censoring scheme incorporating binomial removal, which enables the random withdrawal of surviving units following each failure, making it more suitable for survival studies. Assuming that the underlying distribution of the test units follows the Nadarajah–Haghighi distribution, we examine both point and interval estimation problems for the model parameters, binomial parameter, and two key survival measures. Maximum likelihood estimation serves as the classical methodology for obtaining point estimates and approximate confidence intervals. For Bayesian estimation, we employ the squared error loss function in conjunction with Markov Chain Monte Carlo sampling techniques. A comprehensive simulation analysis is conducted to assess the performance of the various point and interval estimators. In addition, to demonstrate the practical relevance of the proposed methodologies in survival analysis, a real-world data application involving the death times of a group of 45 gastric cancer patients is investigated.OPEN ACCESS Received: 02/11/2025 Accepted: 11/12/2025 Published: 21/07/2026