Inverse Hamza Distribution: Properties and Applications to Lifetime Data
Okpala I. Frank
Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria.
Happiness O. Obiora-Ilouno
Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria.
Omoruyi A. Frederick *
Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria.
*Author to whom correspondence should be addressed.
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.
Keywords: Hamza distribution, inverse hamza, inverted ishita distribution, inverted lomax distribution, inverted lindley distribution, quantile function, lifetime data, order statistics