Inverse Power Akash Probability Distribution with Applications

Abstract

This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-tailed data than Akash, inverse Akash and power Akash distributions respectively.

Useful Extensions of the Juchez Probability Distribution: Properties and Application

“…In like manner, Power Lindley distribution Ghitany [7] was observed to model outcomes that exhibit similar characteristics. Murthy and Jiang [8], Shanker [9], Enogwe [10,11], Shukla and Shanker (2018), Abebe and Shanker [12] proposed Power Exponential Distribution, Power Shanker distribution, Power Hamza distribution, Power Ishita distribution, two parameter Power Rama distribution and Power Garima distribution. As studied, the hazard function of these power distributions exhibit similar shape tendencies which include monotonically increasing and or decreasing failure rate.…”