Revisiting Sen's inequalities on order statistics
Sen [1970. A note on order statistics for heterogeneous distributions. Ann. Math. Statist. 41, 2137-2139] derived some inequalities for distributions of order statistics from independent and non-identically distributed (INID) random variables. For this purpose, he used Hoeffding's [1956. On the distribution of the number of successes in independent trials. Ann. Math. Statist. 27, 713-721] inequality concerning distributions of convolutions of Bernoulli random variables. In this note, we present an alternate proof for Sen's inequalities which also leads to various generalizations.
Year of publication: |
2008
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Authors: | Balakrishnan, N. ; Balasubramanian, K. |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 78.2008, 6, p. 616-621
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Publisher: |
Elsevier |
Keywords: | Order statistics Hoeffding's inequality Sen's inequalities AM-GM inequality INID case Generating function Majorization |
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