Recurrence relations for moments of order statistics from half logistic-geometric distribution and their applications

The half logistic-geometric (HLG) distribution derived here is a simple distribution with interesting properties and is therefore a useful distribution for analyzing lifetime data. Algorithm is derived for the computation of single and product moments of order statistics from this distribution. These recurrence relations enable the computation of means, variances and covariances of all order statistics for all sample size in a simple and efficient way. The results are of great importance in determining the best linear unbiased estimator of the scale parameter of a scaled-HLG distribution, and those of parameters of the more general location-scale HLG distribution based on complete and Type-II censored samples. Finally, an example is presented to illustrate the developed results.