Some Inequalities for Certain Functions of Order Statistics from IFR Distributions.
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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In the paper the authors consider functions which are the sum of the k largest order statistics in a sample of size n from a continuous distribution F , minus nh , where h is a specified constant. If F is an exponential distribution, then for a specified value of k the authors obtain that value of n which maximizes the expected value of the function defined above. If F is IFR then the authors obtain an upper bound on that value of n which maximizes the expected value of the function for a specified value of k, and also an upper bound on the maximum of the expected value of the function. Some other inequalities are also obtained. Author
- Statistics and Probability