On Square Lindley Pareto Distribution: Simulations and Applications

A. In this work, we introduce a new lifetime distribution called the Square Lindley Pareto (SLP) distribution and explore its fundamental properties.Particular attention is given to the cumulative distribution function, as well as the monotonic behavior of the probability density and hazard rate functions.We also derive expressions for the moment-generating function, moments (including mean and variance), stress-strength reliability, mean deviations, Rnyi and Shannon entropy, the quantile function, and extreme order statistics.Furthermore, a comprehensive simulation study is conducted to evaluate the performance of five parameter estimation methods: maximum likelihood estimation (MLE), Anderson-Darling, Cramr-von Mises, maximum product of spacings, and least squares.The estimators are compared based on average absolute bias, mean squared error, and mean absolute relative error.To illustrate the flexibility and practical applicability of the proposed distribution, we analyze four different real-world data sets.The results confirm the SLP distribution's strong modeling capability and its usefulness in various applied fields such as reliability and survival analysis.