MODİFİED ZLİNDLEY DİSTRİBUTİON:STATİSTİCAL PROPERTİES, SİMULATİON AND APPLİCATİONS İN SCİENCES

Abstract

Probability distributions play a crucial role in data-driven decision-making. Their applications span diverse fields, including physics, computer science, public health, medicine, insurance, reliability analysis, life analysis, signal processing, communications, and engineering, which demonstrate the need for more flexible distribution models to capture the complexity of various data sets, such as those in finance, economics, bioengineering, medicine, computer science, and computational science. This study introduces a new two-parameter Power ZLindley distribution that extends the existing ZLindley distribution. The proposed model can accommodate both left-symmetric and left-skewed data sets. The study will discuss the shape characteristics of the Power ZLindley distribution. Furthermore, it provides an analysis of the survival and hazard functions, quantile functions, moment generation functions, mean lifetime functions, Rényi entropy, and order statistics. Statistical features, such as modes, moments, quantile functions, and moment generator functions, are generated to accurately represent the utility of the proposed distribution. The parameters are estimated using the maximum likelihood estimation method. An extensive simulation study is conducted to evaluate the effectiveness of these proposed estimators using MLE for different parameter values. The new proposed distribution is demonstrated to be applicable and flexible through the use of two real-world datasets. Data fitting, simulation studies, and plotting are other statistical inferences on the Power ZLindley distribution provided using R and Maple software.