Inferences based on generalized order statistics under truncated type-I generalized logistic distribution

Abstract

In this paper, estimation of the parameters of a truncated type-I generalized logistic distribution TTIGL(β,α, τ) when β=0 is obtained based on a doubly truncated sample of generalized order statistics. This model is introduced by AL-Angary [Truncated logistic distributions as lifetime models, M.Sc. thesis, Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia, 1997] and the finite mixture of the TTIGL(β,α, τ) component model studied by Ateya [Mixtures of logistic distributions as life-time models, M.Sc. thesis, Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt, 2001] and AL-Hussaini and Ateya [Maximum likelihood estimations under a mixture of truncated type I generalized logistic components model, J. Statist. Theory Appl. 2(1) (2003), pp. 47–60; Bayes estimations under a mixture of truncated type I generalized logistic components model, J. Statist. Theory. Appl. 4(2) (2005), pp. 183–208]. The maximum-likelihood and Bayes methods are used in the estimation and then we compare these methods by computing the mean-squared errors of the estimates in both two cases considering order statistics and upper record values cases. Also, the Bayesian prediction intervals for the future generalized order statistics are computed based on one-sample scheme.