The Effciency Of The Sampling Design From The Inverse Gaussian Distribution

The purpose of statistical inference is to make a more accurate judgment,on the problems studied by extracting sample information.At present,the way to obtain samples usually use simple random sampling(SRS),that is,random sampling from the population.Up to now,the sampling theory derived from SRS has been quite perfect and mature.but if we want to make the samples of SRS more representative,must need a larger sample size.However,in real life,due to the limitation of funds,time or other factors,it is not realistic for us to measure a large number of samples.So,effective sampling design will be an important research topic.In terms of statistical inference,ranked set sampling(RSS)is regarded as an effective method to collect data.R.SS was originally proposed by Australian agriculturist McIntyre(1952,2005)when estimating farm forage yield,because of its high efficiency,it has been widely used in agriculture,environment,medicine and quality control.However,it is easy to make errors when ranking,which due to efficiency dec line.In order to reduce ranking errors and retain RSS excellent sampling properties,Samawi et al.(1996)proposed extreme rankrd set sampling(ERSS).In subsequent studies,Muttlak(1997)proposed median ranked set sampling(MRSS).Bhoj(2001)proposed ranked set sampling with unequal samples in each set in order to better adapt to the needs of reality,Then Biradar and Santosha(2014)proposed Maxiumu ranked set sampling with unequal samples(MRSSU).After these sampling methods based on RSS were proposed,many scholars carried out in-depth studies on them.In this paper,the validity of Inverse Gaussian(IG)distribution under different ranking set sampling is studied.To develop and supplement the sampling theory of RSS IG distribution.The main content is divided into the following aspects:(1)The Fisher information matrix of IG distribution under RSS is obtained.Numerical results show that ranked set samples carry more valid information than simple random samples.(2)The Fisher information matrix of IG distribution under MRSS is obtained.Numerical results show that median ranked set samples carry more valid information than simple random samples.(3)The Fisher information matrix of IG distribution under ERSS is obtained.Numerical results show that extreme ranked set samples carry more valid information than simple random samples.(4)The existence and uniqueness of the maximum likelihood estimator(MLE)of parameters in MRSSU of IG distribution is proved,and the Fisher information matrix of the distribution is obtained.The numerical results show that MLEs under MRSSU is consistently superior to MLEs under SRS.(5)In addition,the Fisher information matrix of simple linear regression model under RSS is obtained.Numerical results show that ranked set samples carry more valid information than simple random samples.In conclusion,ranked set samples is consistently superior to simple random samples in parameter inference of IG distribution and simple linear regression model.