Order Statistics and some of their Properties from the Exponential Pareto Distribution

Abstract

Exponential Pareto (EP) distribution introduced by Al-Kadim and Boshi [1] have received further generalizations from some authors and the new distributions has been proved to exhibit
flexible potentials for modeling real life datasets. However the roles and importance of statistical tools of order statistics from the EP distribution have not been considered, this study investigated the stochastic ordering properties, moments of order statistics and some distributional properties. Distributions of the extrema order statistics, the sample range Rn = X(n:n)−X(1:n) statistics and the rth order statistics was derived for the EP distribution. Explicit expressions and recurrence relations were established for the moments of order statistics, the study obtained some new results for the variability ordering between order statistics in two unequal sample sizes n and m for various combinations of even and odd samples. Distribution of the sample range statistics Rn generalizes and strengthened results for the exponential distribution existing in the literature. Numerical results were tabulated for the mean of order statistics,
the variance, skewness and kurtosis for a sample of size n = 5. The results were used to establish some ordering and statistical properties of order statistics for the exponential Pareto
distribution.