Alpha-Power Exponentiated Inverse Rayleigh distribution and its applications to real and simulated data

• Published in: PloS one Vol. 16; no. 1; p. e0245253
• Main Authors: Ali, Muhammad, Khalil, Alamgir, Ijaz, Muhammad, Saeed, Noor
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 14-01-2021; Public Library of Science (PLoS)
• Subjects: Alpha rays; Data structures; Distribution (Probability theory); Drafting software; Editing; Electric power distribution; Electronic mail; Entropy (Information theory); Failure rates; Flexibility; Mathematical models; Mean; Parameter estimation; Physical Sciences; Probability distribution; Random variables; Rayleigh distribution; Research and Analysis Methods; Reviews; Statistical analysis; Statistics; Weibull distribution; Pakistan; Peshawar Pakistan
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0245253

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.