Advances and Applications in Statistics
Volume 28, Issue 2, Pages 141 - 147
(June 2012)
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DIFFERENCE BETWEEN SAMPLE MEDIAN AND POPULATION MEDIAN WITH ODD SAMPLE SIZES
Ali Akbar Rahimzadeh Sani, Hamid Reza Mostafaei and Mahdiyeh Ghohyeei
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Abstract: In this article, the efficiency of the sample median, as an estimator of the population median, has been discussed thoroughly.
We define the Pitman closer estimator and the Pitman closest estimator and consider the result of Pitman closeness of the sample median to population median than the order statistics in the symmetric distributions. We show that by Pitman’s measure of closeness (PMC) criterion, the median with 2m sample sizes is closer to population median than the sample median with sample sizes and also discuss that the median with sample sizes is closer to the population median than the sample median with sample sizes by this method. We determine the Pitman closer estimator in two previous cases through probabilistic derivations, in other words, in comparing sample medians for the symmetric distributions, if one or two observations are added to the sample with odd sample sizes, in this case, the sample median with new sample sizes is a Pitman closer estimator than the previous median, so the median with new sample size is a good estimator of population median. |
Keywords and phrases: Pitman closer, closeness probability, odd sample, Pitman’s measure of closeness, sample median |
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