Development and Estimation of Weighted Xgamma Exponential Distribution with Applications to Lifetime Data

Abstract

In this article, we introduce a weighted version of the Xgamma exponential distribution, extending its utility in modeling lifetime data. We derive several important distributional properties of the proposed model, including moments, residual life functions, generating functions, stochastic ordering, aging intensity, and entropy. These properties provide deeper insights into the behavior and structure of the proposed distribution. To estimate the model parameters, we discuss the maximum likelihood estimation approach, focusing on complete sample data. To demonstrate the practical applicability of the proposed distribution, we analyze two real-world lifetime data sets. The performance of the weighted Xgamma exponential distribution is compared with several well-established one- and two-parameter lifetime distributions, along with their weighted versions. Additionally, comparisons are made with length-biased and area-biased lifetime distributions to further assess the robustness of the proposed model. The results of these comparisons indicate that the proposed weighted distribution offers a superior fit, particularly for data sets exhibiting an increasing failure rate. The model’s ability to outperform competing distributions highlights its potential as an effective alternative for analyzing lifetime data in reliability and survival studies.