Extension of Exponential Pareto Distribution to form Exponential Pareto Negative Binomial Distribution with its Properties and Application

Abstract

Mixing distribution has been a special research activity in industry due to its economic, social and developmental relevance. In this research, Exponential Pareto Negative Binomial Distribution was developed by compounding the Exponential Pareto with the Negative Binomial Distribution. Compounding two or more probability distributions, we get the corresponding hybrid distribution with increased number of parameters which is believed to give the newly compounded distribution more flexibility, consistency, stability, sufficiency, uniqueness and wider applicability as compare to its parent distribution. Some basic properties of the newly proposed distribution including moments, moment generating function, survival rate function, hazard rate function and the estimation of parameters have been studied. The estimation of the model parameters is performed by the maximum likelihood method. The plot of the density showed that the Exponential Pareto Negative Binomial Distribution (EPNBD) has mode which could be unimodal, bimodal or multimodal. It is also heavily tailed, heavily skewed and leptokurtic indicating that the model can be used to track aprocess with non-normal distributed population. From analysis, Exponential Pareto Negative Binomial Distribution provides good fit as compared to existing Weibull Negative Binomial Distribution [WNBD] distributions based on failure data obtained from cooling system, also, Akaike Information Criteria used still established the fact that EPNBD performed better than WNBD. Then the model should be used by researchers and statistician that are in this area in taking any prospective decision among others. Keyword: Exponential distribution, Weibull Negative Distribution, moment estimation.