Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset

The Exponential Pareto (EP) model has been extended by applied and theoretical statisticians for wider applications and new knowledge using different techniques but the Weibull-X technique has not been considered. This article proposed a new extension of the EP model called the Weibull-Exponential Pareto (WEP) distribution to provide better modeling that fits real-life datasets and to explore the statistical theory of order statistics from the proposed distribution. Statistical properties investigated include the Shannon and Renyi entropies; the moments and moment generating function. Distribution of order statistics and the moment of order statistics were derived including the mean and variance of order statistics. WEP distribution has unimodal, decreasing, and increasing failure rates; and it can be negatively or positively skewed and approximately symmetric with the potential for fitting platykurtic, mesokurtic, and leptokurtic lifetime data. The parameters of the distribution were estimated using the method of maximum likelihood estimation (MLE), which was examined for consistency through a simulation study. The performance of the proposed distribution was investigated by application to flood peaks exceedances and some lifetime datasets from engineering. The results from data analysis using the R-software revealed that the WEP distribution has the potential to provide a superior model that fits the three data sets better than some notable existing distributions and previous extensions of the EP model in the literature. The statistical property of order statistics extended in the study established some important results that characterized some notable lifetime distributions in the literature.