Inference on Exponentiated Power Lindley Distribution Based on Order Statistics with Application

Exponentiated power Lindley distribution is proposed as a generalization of some widely well-known distributions such as Lindley, power Lindley, and generalized Lindley distributions. In this paper, the exact explicit expressions for moments of order statistics from the exponentiated power Lindley distribution are derived. By using these relations, the best linear unbiased estimates of the location and scale parameters, based on type-II right-censored sample, are obtained. Next, the mean, variance, and coefficients of skewness and kurtosis of some certain linear functions of order statistics are calculated and then used to derive the approximate confidence interval for the location and scale parameters using the Edgeworth approximation. Finally, some numerical illustrations and two real data applications are presented.

Edgeworth Approximation of Multivariate Differential Entropy

We develop the general, multivariate case of the Edgeworth approximation of differential entropy and show that it can be more accurate than the nearest-neighbor method in the multivariate case and that it scales better with sample size. Furthermore, we introduce mutual information estimation as an application.

Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models

We examine the higher order asymptotic properties of semiparametric regression estimators that were obtained by the general MINPIN method described in Andrews (1989, Semiparametric Econometric Models: I. Estimation, Discussion paper 908, Cowles Foundation). We derive an order n−1 stochastic expansion and give a theorem justifying order n−1 distributional approximation of the Edgeworth type.