Higher Order Moments of Order Statistics From the Power Function Distribution and Edgeworth Approximate Inference

In this paper, we first derive exact explicit expressions for the triple and quadruple moments of order statistics from the power function distribution. Also, we present recurrence relations for single, double, triple and quadruple moments of order statistics from the power function distribution. These relations will enable one to find all moments (of order up to four) of order statistics for all sample sizes in a simple recursive manner. We then use these results to determine the mean, variance, and coefficients of skewness and kurtosis of certain linear functions of order statistics. We then derive approximate confidence intervals for the parameters of the power function distribution using the Edgeworth approximation. Finally, we extend the recurrence relations to the case of the doubly truncated power function distribution.