2 Higher order moments of order statistics from exponential and right-truncated exponential distributions and applications to life-testing problems

Publisher This chapter discusses the concept of higher order moments of order statistics from exponential and right-truncated exponential distributions and its applications to life-testing problems. It presents several recurrence relations satisfied by the single, double, triple, and quadruple moments of order statistics from the standard exponential distribution, respectively. It considers the scale-parameter exponential distribution and use the results derived to determine the mean, variance, and coefficients of skewness and kurtosis of the best linear unbiased estimator of the scale parameter based on doubly Type-II censored samples. While it is well known that for the case when the available sample is Type-II right censored the best linear unbiased estimator of the scale parameter has exactly a chi-square distribution, the chapter shows that a chi-square distribution provides a very close approximation to the distribution of the best linear unbiased estimator even when the available sample is doubly Type-II censored. The chapter also discusses three examples involving life-testing data and illustrates the usefulness of the chi-square approximation for the distribution of the best linear unbiased estimator by constructing approximate confidence intervals for the mean life-time.