Parametric Estimation For The Log-extended Exponential-geometric Distribution Under The Optimal Sampling Design

An effective method to obtain data not only plays an important role in the development of sampling theory but also has immediate significance.Ranked set sampling(RSS)was first proposed by Australian agriculturist McIntyre with the purpose of estimating the pasture yields.As a cost effective method to collecting data,RSS has been wildly used in various fields such as agriculture,environment and medical.The current paper devotes to seek optimal sampling designs and op-timal estimators for the Log-extended exponential-geometric(LEEG)distribution:(1)Initially,for the LEEG distribution which only take shape parameter?(?=0),namely Power-law distribution,the optimal estimators of a are s-tudied based on RSS.Further,a new RSS version based on the order statistic that maximizes the Fisher information number for the Power-law distribution is founded and the optimal estimators based on this RSS are studied.The situation of imperfect ranking is also considered in simulation.The simulation results show whether perfectranking or not the estimators under RSS are more efficient than the ones under simple random sampling(SRS).(2)For the LEEG distribution take both shape parameter ? and scale param-eter ?(??0),in order to choose optimal sampling designs which can inference the parameters of LEEG distribution efficiently from the three kinds of classical RSS in existence,the Fisher information matrixes based on balanced RSS,medi-an RSS(MRSS),extreme RSS(ERSS)were respectively calculated.A simulation and real data application show that:the efficiency of the three kinds of RSS are obviously better than that of SRS.Thereinto,to inference one parameter when the other is known,the samples of MRSS perform better;But for the parameters inference when both parameters are unknown,the balanced RSS is more efficient.(3)Eventually,the current paper using moving extreme ranked set sam-pling(MERSS)respectively studied the optimal estimators for the Power-law dis-tribution and the efficiency of parameter inference for the LEEG distribution to reduce the probability of ranking error.Both simulation and real data application results show that MERSS is more efficient than SRS to estimate the parameter(s)for the two distributionsIn a word,RSS is significantly more efficient than SRS for the parameter inference of the LEEG distribution.