Inverse Hamza Distribution: Properties and Applications to Lifetime Data

Abstract

In this paper, a new distribution, named ‘the Inverted Hamza distribution’, was introduced.  It is an extension of the Hamza distribution that can model real-world data with an upside-down bathtub shape and heavy tails.  Mathematical and statistical characteristics such as the quantile function, moments, entropy measure, stochastic ordering and distribution of order statistics have been derived. Furthermore, dependability measures such as the survival function and hazard function have been developed. The greatest likelihood technique was used to estimate the distribution parameters. To demonstrate the applicability of the distribution, a numerical example was given. According on the results, the proposed distribution outperformed the competing distributions.