Open AccessAlpha-Power Exponentiated Inverse Rayleigh distribution and its applications to real and simulated data
Author(s) -
Muhammad Ali,
Alamgir Khalil,
Muhammad Ijaz,
Noor Saeed
Publication year - 2021
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0245253
Subject(s) - rayleigh distribution , quantile , mathematics , monotonic function , statistics , quantile function , order statistic , inverse distribution , probability distribution , heavy tailed distribution , cumulative distribution function , probability density function , statistical physics , mathematical analysis , physics
The main goal of the current paper is to contribute to the existing literature of probability distributions. In this paper, a new probability distribution is generated by using the Alpha Power Family of distributions with the aim to model the data with non-monotonic failure rates and provides a better fit. The proposed distribution is called Alpha Power Exponentiated Inverse Rayleigh or in short APEIR distribution. Various statistical properties have been investigated including they are the order statistics, moments, residual life function, mean waiting time, quantiles, entropy, and stress-strength parameter. To estimate the parameters of the proposed distribution, the maximum likelihood method is employed. It has been proved theoretically that the proposed distribution provides a better fit to the data with monotonic as well as non-monotonic hazard rate shapes. Moreover, two real data sets are used to evaluate the significance and flexibility of the proposed distribution as compared to other probability distributions.