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, Kindom of Saudi Arabia,1997] and the finite mixture of TTIGL(β, α, τ ) component model studied by [Ateya,Mixtures of logisticdistributions 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. Stat. Theory Appl. 2(1) (2003), pp. 47–60; AL-Hussaini and Ateya, Bayes estimations under a mixture of truncated type I generalized
logistic components model, J. Stat. Theory Appl. 4(2) (2005), pp. 183–208]. The maximum-likelihood andBayes methods are used in the estimation and then we compare these methods by computing the mean
squared errors of the estimates in both cases considering orderstatistics and upper record values cases. Also, the Bayesian prediction intervals for the future generalized order statistics are computed based on a one-sample scheme