On some Aspects of Generalized Order Statistics

Abstract

The present thesis entitled On Some Aspects of Generalized Order newlineStatistics is based on six chapters. newlineChapter I is introductory in nature. This chapter consists of those newlineconcepts and results like order statistics, record values, generalized order statistics and lower generalized order statistics, which are used in newlinesubsequent chapters. newlineChapter II deals with the relations for moments of generalized order newlinestatistics from type-I generalized half logistic distribution. Further, the newlineresults are deduced for moments of order statistics and record values and newlinea characterization of this distribution has been considered on using the newlineconditional moments of the generalized order statistics. newlineChapter III contains relations for moments of generalized order statistics newlinefrom marshall-olkin log-logistic distribution. Further, some of its newlineimportant deductions and particular cases are discussed and a characterizing results of this distribution has been obtained using conditional moments of generalized order statistics, also some computational work are carried out. newlineChapter IV is based on the explicit expression and recurrence relation for newlinemoment of generalized order statistics from exponentiated exponentialgeometric newlinedistribution. Further, the results are derived for moments of order statistics and lower record values and two theorems for characterizing generalized exponential distribution are stated and proved, newlinealso some computational work are carried out. newlineChapter V embodies relations for moment generating functions for lower newlinegeneralized order statistics from generalized exponential distribution. newlineFurther, the distribution is characterized using conditional moments of lower generalized order statistics. Also some deductions and particular cases are given. newlineChapter VI is based on quotient moments for lower generalized order statistics from Dagum distribution. Further, the distribution is characterized using conditional moments of lower generalized orderstatistics. Also some deductions and particular cases are given.