The Generalized Alpha Power Exponentiated Inverse Exponential distribution and it's application to real data

Abstract

This paper proposes a new distribution named “The Generalized Alpha Power Exponentiated Inverse Exponential (GAPEIEx for short) distribution” with four parameters, from which one (1) scale and three (3) shape parameters and the statistical properties such as Survival function, Hazard function, Quantile function, r^(th) Moment, Rényi Entropy, and Order Statistics of the new distribution are derived. The method of maximum likelihood estimation (MLE) is used to estimate the parameters of the distribution. The performance of the estimators is assessed through simulation, which shows that the maximum likelihood method works well in estimating the parameters. The GAPEIEx distribution was applied to simulated and real data in order to access the flexibility and adaptability of the distribution, and it happens to perform better than its submodels.