4 Recurrence relations for single and product moments of order statistics from a generalized logistic distribution with applications to inference and generalizations to double truncation

Publisher This chapter discusses the recurrence relations for single and product moments of order statistics from a generalized logistic distribution with applications to inference and generalizations of double truncation. It establishes several recurrence relations satisfied by the single moments and the product moments. These recurrence relations enable to compute all the single and product moments of order statistics for all sample sizes in a simple recursive manner. If the shape parameter k → 0, the recurrence relations reduce to the corresponding results for the logistic distribution established by Shah. The chapter discusses the quantities that have been used to determine the best linear unbiased estimators (BLUEs) of the location and scale parameters of the generalized logistic distribution and the necessary tables of coefficients and the variances and covariance of the BLUEs have been tabulated for sample sizes 5(5)20 for k = 0.1(0.1)0.4. It also discusses maximum likelihood estimation for the two-parameter and the three-parameter models based on Type-II right censored samples. For the generalized logistic distribution, the chapter presents an example to illustrate these methods of inference.