Generalized secant hyperbolic order statistics and associated inferences

Abstract

In this article, we consider the generalized secant hyperbolic (GSH) distribution with known shape parameter t. Exact expressions for single and product moments of order statistics are established. The expressions are represented in terms of Riemann zeta, polygamma and hypergeometric functions. These special functions allow us to use a series of Mathematica procedures that will compute the means, variances and covariances of order statistics from the GSH distribution. The so-obtained values are used to compute the coefficients of the best linear unbiased estimators of the location and scale parameters. The variances of these estimators are also presented. A real data set has been performed to illustrate our findings.