3 Log-gamma order statistics and linear estimation of parameters

Publisher This chapter discusses log-gamma order statistics and the linear estimation of parameters. By assuming that the shape parameter κ is known, the chapter discusses the best linear unbiased estimation of the location parameter and the scale parameter on complete and Type-II censored samples. It provides the necessary tables for complete and right-censored samples for sample sizes up to twenty five and κ = 0.5(0.5)2.0(1.0)4.0(2.0)12.0. This is made possible after determining the single and product moments of order statistics in terms of digamma and trigamma functions and then computing the means, variances, and covariance of order statistics. The chapter also considers a life-test data given by Lawless and illustrates the method of estimation.