A Study on Exponential Poisson Lindley Distribution, Properties, Simulations and its Application in Engineering

This study extends the continuous Poisson Lindley distribution with the aid of an existing link function, the Exp-G family. It studied the probability density function (pdf) and the cumulative distribution function (cdf) of the new Extended Poisson Lindley distribution (ExPLinD) and presents appropriate plots. Statistical Properties of the ExPLinD were studied and presented. Some of these properties include its moments, moment generating function (mgf), characteristics function and quantile function. Reliability studies was carried out and relevant charts showing the plot of the survival function and hazard functions were presented. The ExPLinD has an increasing hazard shape among others displayed in the hazard shape plots, this makes the distribution useful in reliability studies. Maximum Likelihood method was employed to estimate the parameters of ExPLinD. Simulation studies of the ExPLinD was done using different parameter values and different sample sizes. Simulation studies of ExPLinD shows that the average estimates of the parameters of ExPLinD tends to the true parameters as sample size increases, this is in order with first order asymptotic theory. The ExPLinD was fitted to an Engineering data and compared to some closely related distributions. It provided a better fit compared to the related distribution which makes it an important distribution in Statistical modeling.