5 Order statistics from the Type III generalized logistic distribution and applications

Publisher This chapter discusses order statistics from the type III generalized logistic distribution and presents its applications. It derives the Type III generalized logistic distribution by compounding an exponential-gamma distribution with a gamma distribution as in Balakrishnan and Leung. It presents a re-parametrized model, which has a standard normal distribution as the limiting distribution as the shape parameter tends to infinity. This re-parametrized model, in addition to being useful as a life-time model, can also serve as meaningful alternative to the normal distribution for robustness studies concerning some classical procedures based on normality. The chapter also discusses the order statistics and moments from this re-parametrized distribution. Tables of means, variances, and covariances of order statistics are presented in the chapter for sample size n = 20 and shape parameter = 0.5(0.5)3(1)6(2)12. The chapter also discusses the best linear unbiased estimators (BLUEs) and the maximum likelihood estimators (MLEs) of the location and scale parameters, respectively. The coefficients of the BLUEs, the variance and covariance factors of the BLUEs, and the simulated values of the bias, variances, covariance, and mean square errors of the MLEs for sample size n = 20 are also presented in the chapter.