A Novel Method for Developing Efficient Probability Distributions with Applications to Engineering and Life Science Data

Alamgir Khalil,Muhammad Ali,Abdullah Ali H Ahmadini,Zabidin Salleh,Shokrya S Alshqaq,Wali Khan Mashwani,Zakia Hammouch

doi:10.1155/2021/4479270

Abstract

In this paper, a new approach for deriving continuous probability distributions is developed by incorporating an extra parameter to the existing distributions. Frechet distribution is used as a submodel for an illustration to have a new continuous probability model, termed as modified Frechet (MF) distribution. Several important statistical properties such as moments, order statistics, quantile function, stress-strength parameter, mean residual life function, and mode have been derived for the proposed distribution. In order to estimate the parameters of MF distribution, the maximum likelihood estimation (MLE) method is used. To evaluate the performance of the proposed model, two real datasets are considered. Simulation studies have been carried out to investigate the performance of the parameters’ estimates. The results based on the real datasets and simulation studies provide evidence of better performance of the suggested distribution.

Highlights

In the last few years, the literature of distribution theory has become rich due to the induction of additional parameters in the existing distribution. e inclusion of an extra parameter has shown greater flexibility compared to competitive models. e inclusion of a new parameter can be performed either using the available generator or by developing a new technique for generating new improved distribution compared to classical baseline distribution
We suggest a new method for obtaining new continuous probability distributions
The Proposed Class of Distributions e proposed class of probability distributions is termed as modified Frechet class (MFC) of distributions. e cumulative distribution function (CDF) and probability density function (PDF) of the suggested class of distributions are given by the following expressions: e− (F(x))α − 1

Summary

Introduction

In the last few years, the literature of distribution theory has become rich due to the induction of additional parameters in the existing distribution. e inclusion of an extra parameter has shown greater flexibility compared to competitive models. e inclusion of a new parameter can be performed either using the available generator or by developing a new technique for generating new improved distribution compared to classical baseline distribution. AlAqtash et al [10] proposed a new class of models using the logit function as a baseline and obtained the particular case referred to as Gumbel–Weibull distribution. E cumulative distribution function (CDF) and probability density function (PDF) of the suggested class of distributions are given by the following expressions: e− (F(x))α − 1. A random variable X is said to have MF distribution with two parameters α and β if its PDF is given as follows: αβx− (β+1)e− αx− β− e− αx− β fMF(x). Substitute PDF and CDF of MF in equation (22), and we obtain distribution of ith order statistic as fi: n(x) Using equation PDF and CDF of MF in the above expression, the stress-strength parameter is given as. Where Zζ is the upper ζth percentile of the standard normal distribution

Simulations’ Studies

Applications

Conclusion