arXiv subjects

Adarsha Kumar Jena

Publications and source records attributed to Adarsha Kumar Jena.

3 recordsLinked to original sources

arXiv2026

Interval Estimation of the Common Shape Parameter and Coefficient of Variation of Several Weibull Populations under Progressive Censoring

The Weibull distribution is one of the most flexible continuous probability distributions used to model various failure rates and skewed data in reliability engineering, industry, weather studies and cancer studies. It is a common scenario in statistical inference that several Weibull populations share the same shape parameter, which also implies that they have the same coefficient of variation. While the inferential study of the common shape parameter is often considered for complete samples, the presence of censored data requires a separate investigation that has not received enough attention in the existing literature. Therefore, the focus of this article is on a comparative study of interval estimators for the common shape parameter and the common coefficient of variation under progressive type-II censoring using frequentist methods based on large-sample theory, variance estimates recovery, generalized pivots, and Bayesian inference. An optimal censoring scheme is also proposed to enhance the robustness of interval estimation. Numerical data analyses using a simulation study and a real carbon fiber strength data example are carried out for comparison, and the results recommend the intervals based on Bayesian and variance estimates recovery methods for their satisfactory performance.

stat.ME↗

arXiv2026

Relative Variability Estimation for the Power Lindley Model with Progressive Type-I Interval Censored Data

The measures of relative variability, such as the coefficient of variation, are estimated for the Power Lindley distribution using progressive type-I interval-censored data. Both Bayesian and frequentist approaches are applied, including the midpoint approximation, maximum likelihood estimation, method of moments, bootstrap, and non-linear least squares methods. Since the closed-form expressions of the parameters are not available, numerical approximation methods have been utilized for parameter estimation. Asymptotic confidence intervals are constructed within the likelihood framework. The percentile and Student-t bootstrap intervals are also proposed. In the Bayesian paradigm, independent informative and non-informative priors are assumed for the parameters, and the posterior point and interval inference have been carried out using the slice sampling algorithm. A discussion on choosing optimal monitoring intervals is also highlighted. A comprehensive simulation study is conducted to evaluate the performance of the proposed estimators across various censoring plans and sample sizes. A real data application illustrates the practical utility of the proposed methodologies. The results indicate that the Bayesian framework generally exhibits superior performance in both point and interval estimation.

stat.ME↗

arXiv2025

Estimation of the Coefficient of Variation of Weibull Distribution under Type-I Progressively Interval Censoring: A Simulation-based Approach

Measures of relative variability, such as the Pearson's coefficient of variation (CV$_p$), give much insight into the spread of lifetime distributions, like the Weibull distribution. The estimation of the Weibull CV$_p$ in modern statistics has traditionally been prioritized only when complete data is available. In this article, we estimate the Weibull CV$_p$ and its second-order alternative, denoted as CV$_k$, under type-I progressively interval censoring, which is a typical scenario in survival analysis and reliability theory. Point estimates are obtained using the methods of maximum likelihood, least squares, and the Bayesian approach with MCMC simulation. A nonlinear least squares method is proposed for estimating the CV$_p$ and CV$_k$. We also perform interval estimation of the CV$_p$ and CV$_k$ using the asymptotic confidence intervals, bootstrap intervals through the least squares estimates, and the highest posterior density intervals. A comprehensive Monte Carlo simulation study is carried out to understand and compare the performance of the estimators. The proposed least squares and the Bayesian methods produce better point estimates for the CV$_p$. The highest posterior density intervals outperform other interval estimates in many cases. The methodologies are also applied to a real dataset to demonstrate the performance of the estimators.

stat.ME↗