An odd property of sample median from odd sample sizes |
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Authors: | G Iliopoulos N Balakrishnan |
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Institution: | 1. Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou Street, 18534 Piraeus, Greece;2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 |
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Abstract: | In this paper, we establish some Pitman closeness results concerning the sample median from a symmetric continuous distribution. We show that when an odd sample size is increased by one, the sample median becomes Pitman-closer to the population median, while when an even sample size is increased by one, the sample median need not be Pitman-closer. We establish the former through probabilistic derivations while the latter is through a counterexample. We also discuss the situation when the sample is increased by two observations. |
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