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.
