Optimal Estimation Of The Parameters For Rayleigh Distribution Under The Optimal Sampling Design

Generalized Rayleigh(GR)distribution was first introduced by Surles and Padgett(2001),GR is a useful distribution in modelling reliability and lifetime data parameters.When ?=1,GR distribution coincides with the Rayleigh distribution.Therefore,the Rayleigh distribution can be regarded as a special form of the GR distribution.Rayleigh distribution is the most common type of distrib ution used to describe the statistical time-varying properties of a flat fading signal reception envelope or an independent multipath component reception envelope.When the actual measurement of the research object is irreparably destructive or costly,effective sampling design will be an important research topic.In terms of statistical inference,Ranked set sampling(RSS)is regarded as an effective way to collect data.RSS was first proposed by Australian agriculturist McIntyre with the purpose of estimating the pasture yields.Because of its high efficiency,RSS has been wildly used in various fields of agriculture,environment and medical.The current paper devotes to seek optimal sampling designs and optimal estimators for the Rayleigh distribution and GR distribution.(1)For the single parameter Rayleigh distribution,a unbiased estimator,a best linear unbiased estimator(BLUE),a maximum likelihood estimation of(MLE)and modified MLE of parameter from Rayleigh distribution in RSS are studied.Then it is compared with the parameter estimation under simple random sampling(SRS)of the same sample size.The numerical results show that the unbiased estimator,BLUE,MLE and the modified MLE of parameter in RSS are significantly more efficient than the ones in SRS.(2)For the two-parameter GR distribution,we considered the Fisher information matrix from GR distribution in RSS.The numerical results show that the moving extremes ranked set sample carry more information about parameters than a simple random sample of equivalent size.based on this a modified unbiased estimator and a modified BLUE of parameters from GR distribution in RSS are studied.The simulation results show the estimators under RSS are more efficient than the ones under SRS.(3)In order to reduce the error of ranking,the optimal estimators of Rayleigh distribution and GR distribution are studied based on moving extreme ranked set sampling(MERSS)and considered the Fisher information matrix from GR distribution in MERSS.The numerical results show that the estimators of parameters in MERSS are significantly more efficient than the ones in SRS,MERSS is more efficient than SRS.In conclusion,for the Rayleigh distribution,the estimators under RSS are more efficient than the ones under SRS;for the GR distribution,the RSS carry more information about parameters than SRS,and the estimators under RSS are more efficient than the ones under SRS.Consider reducing the error of ranking,the estimators under RSS and MERSS are more efficient than the ones under SRS,and MERSS carry more information about parameters than SRS.So for both the Rayleigh distribution and the GR distribution,RSS and MERSS is more efficient than SRS,and the estimators under RSS and MERSS are more efficient than the ones under SRS.