Reliability Modeling using an Equilibrium-Based Xgamma Distribution: Properties, Estimation, and Applications
- 1Assistant Professor, Presidency University, Kolkata
- 2Department of Statistics, Visva Bharati University
- 3Department of Statistics, Siliguri College
Abstract
The equilibrium distribution approach is applied to the existing Xgamma model in this work to develop a new lifetime model known as the Induced Xgamma (i-Xg) distribution. Because of its adaptable shape properties, the suggested distribution can be used to model heterogeneous and positively skewed lifetime datasets. Probability density and distribution functions, moments, the moment generating function, reliability measures (mean residual life, hazard rate, and reversed hazard), stochastic dominance, entropy measures, inequality curves, and order statistics, including extremes, are among the important analytical properties that we derive. The model's identifiability is rigorously established. The model parameter is estimated using seven traditional estimation methods: Maximum Likelihood (ML), Least Squares (LS), Weighted LSE (WLS), Cramer-von-Mises (CvM), Maximum Product of Spacings (MPS), Anderson-Darling (AD), and Right-tail AD (RAD). Their performance is assessed in terms of bias and MSE for varying sample sizes using a Monte-Carlo simulation study. The suggested i-Xg model provides a better fit than competing distributions, as shown by applications to a variety of real-life datasets, confirming its value in statistical modelling of survival-type and reliability data.
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BibTeX
@article{ruidas2026reliability,
title = {{Reliability Modeling using an Equilibrium-Based Xgamma Distribution: Properties, Estimation, and Applications}},
author = {Molay Ruidas and Sudhansu S Maiti and Sukanta Pramanik},
journal = {Reliability: Theory \& Applications},
year = {2026},
month = sep,
doi = {10.66721/99jshb97},
url = {https://doi.org/10.66721/99jshb97},
note = {CC BY-NC},
}
RIS
TY - JOUR
TI - Reliability Modeling using an Equilibrium-Based Xgamma Distribution: Properties, Estimation, and Applications
AU - Molay Ruidas
AU - Sudhansu S Maiti
AU - Sukanta Pramanik
PY - 2026
DA - 2026/09/01
JO - Reliability: Theory & Applications
DO - 10.66721/99jshb97
UR - https://doi.org/10.66721/99jshb97
AB - The equilibrium distribution approach is applied to the existing Xgamma model in this work to develop a new lifetime model known as the Induced Xgamma (i-Xg) distribution. Because of its adaptable shape properties, the suggested distribution can be used to model heterogeneous and positively skewed lifetime datasets. Probability density and distribution functions, moments, the moment generating function, reliability measures (mean residual life, hazard rate, and reversed hazard), stochastic dominance, entropy measures, inequality curves, and order statistics, including extremes, are among the important analytical properties that we derive. The model's identifiability is rigorously established. The model parameter is estimated using seven traditional estimation methods: Maximum Likelihood (ML), Least Squares (LS), Weighted LSE (WLS), Cramer-von-Mises (CvM), Maximum Product of Spacings (MPS), Anderson-Darling (AD), and Right-tail AD (RAD). Their performance is assessed in terms of bias and MSE for varying sample sizes using a Monte-Carlo simulation study. The suggested i-Xg model provides a better fit than competing distributions, as shown by applications to a variety of real-life datasets, confirming its value in statistical modelling of survival-type and reliability data.
SN - 1932-2321
ER -