Inference on parameters of the Laplace distribution based on Type-II censored samples using Edgeworth approximation

By deriving two recurrence relations which express the single and double moments of order statistics from a symmetric distribution in terms of the corresponding quantities from its folded distribution, Govindarajulu (1963, 1966) determined means, variances and covariances of Laplace order statistics (using the results on exponential order statistics) for sample sizes up to 20. He also tabulated the BLUE's (Best Linear Unbiased Estimators) of the location and scale parameter of the Laplace distribution based on complete and symmetrically Type-II censored samples. In this paper, we first establish similar relations for the computation of triple, and quadruple moments. We then use these results to develop Edgeworth approximations for some pivotal quantities which will enable one to develop inference for the location and scale parameters. Next, we show that this method provides close approximations to percentage points of the pivotal quantities determined by Monte Carlo simulations. Finally, we present an example to illustrate the method of inference developed in this paper.