Higher order moments of record values from the Inverse Weibull lifetime model and Edgeworth approximate inference

Abstract

In this paper, we derive exact explicit expressions for the triple and quadruple moments of the lower record values from inverse the Weibull (IW) distribution. Next, we present and calculate the co- e±cients of the best linear unbiased estimates of the location and scale parameters of IW distribution (BLUEs) for di®erent choices of the shape parameter and records size. We then use the higher order moments and the calculated BLUEs to compute the mean, variance, and the coe±- cients of skewness and kurtosis of certain linear functions of lower record values. By using the coe±cients of the skewness and kurtosis, we develop approximate con¯dence intervals for the location and scale parameters of the IW distribution using Edgeworth approximate values and then com- pare them with the corresponding intervals constructed through Monte Carlo simulations. Finally, we apply the ¯ndings of the paper to some simulated data.