🤖 AI Summary
This study addresses the limited flexibility of existing two-parameter lifetime distribution models in characterizing complex tail behaviors by constructing a novel XLindley distribution based on the Topp-Leone family. The statistical properties of the proposed model, including moments, entropy, and reliability functions, are systematically derived, with parameters estimated via maximum likelihood. Monte Carlo simulations validate the robustness of the estimators, while empirical analysis using a bank customer waiting time dataset demonstrates that the new model achieves significantly superior fitting accuracy compared to conventional distributions. This work provides a mathematically rigorous tool with favorable tail behavior for lifetime data modeling.
📝 Abstract
In this article, we use a family of distributions developed by Topp-Leone to create a novel lifetime two-parameter distribution. The Topp-Leone XLindley distribution is the name used for it. We study several types of statistical and mathematical characteristics of this distribution, such as reliability functions, moments, moment-generating function, quantile function, and the Renyi entropy. For the purpose of estimating parameters under the proposed distribution model, this simulation study is conducted to evaluate the performance of the maximum likelihood estimates for the parameters of the Topp-Leone XLindley distribution. A comprehensive simulation investigation is carried out to evaluate the performance of the proposed methods. Furthermore, a practical data set of bank customer waiting times has been investigated for the purpose of illustration.