InterStat 2006 http://interstat.statjournals.net A note on Des Raj’s ordered estimator for SRSWOR Soubhik Chakraborty* Kiran Kumar Sundararajan Lopamudra Ray Saraswati Population System Analysis Chandan Bandyopadhyay Infotech Enterprises Limited University Department of Statistics Infocity And Computer Applications Hyderabad – 500 033 T. M. Bhagalpur University India Bhagalpur-812007 India *Email address of the communicating author: soubhikc@yahoo.co.in Abstract: This note shows Des Raj’s ordered estimator can be easily constructed for srswor. We next prove its unbiasedness and give its variance expression. A C- code on a popular srswor algorithm that takes order into account with run time results is also provided. Key words: Des Raj’s ordered estimator, srswor Section I Introduction: Let x 1 , x 2 …x n be a random sample of size n obtained by simple random sampling without replacement (srswor) from a population of size N where x i occurs in the i-th draw, i=1, 2,….,n. We all know that under srswor the probability of any of the available units in the population after (i-1) draws to be included in the sample in the i-th draw is1/(N-i+1) where i=1, 2…n. Now define a statistic z m = (z 1 + z 2 +…z n )/n…(1) Where z 1 = Nx 1 z 2 = x 1 + Nx 2 (1-1/N) = x 1 + x 2 (N-1) and in general, z i = (x 1 + x 2 +….x i-1 ) + x i (N-i+1), i= 2, 3…n let X.. be the population total. Clearly the statistic z m takes the order of arrival of the sampled observations into account in addition to the values of the sampled observations. We argue that z m is Des Raj’s ordered estimator re-defined for srswor case. Des Raj originally defined it for pps(a kind of varying probability) sampling(see ref[1]). Claim 1: z m is an unbiased estimator for estimating X.. Proof: We have, E(z 1 )=NE(x 1 )=X.. since E(x 1 )=Population mean=X../N 1