MOMENTS OF LOWER GENERALIZED ORDER STATISTICS FROM DOUBLY TRUNCATED CONTINUOUS DISTRIBUTIONS AND CHARACTERIZATIONS

In this paper, we derive recurrence relations for mo- ments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, gen-eralized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribu- tion based on single moments of lower generalized order statistics are given.