Poisson Exponential Power Distribution: Properties and Application

In this study, we have established a new three-parameter Poisson Exponential Power distribution using the Poisson-G family of distribution. We have presented the mathematical and statistical properties of the proposed distribution including probability density function, cumulative distribution function, reliability function, hazard rate function, quantile, the measure of skewness, and kurtosis. The parameters of the new distribution are estimated using the maximum likelihood estimation (MLE) method, and constructed the asymptotic confidence intervals also the Fisher information matrix is derived analytically to obtain the variance-covariance matrix for MLEs. All the computations are performed in R software. The potentiality of the proposed distribution is revealed by using some graphical methods and statistical tests taking a real dataset. We have empirically proven that the proposed distribution provided a better fit and more flexible in comparison with some other lifetime distributions.