APPROXIMATE JOINT PROBABILITIES FOR LARGEST AND SMALLEST OF A SET OF INDEPENDENT OBSERVATIONS.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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Let X sub n and X sub 1 be the largest and smallest, respectively, of a set of n independent observations. Also, let F bar xn be the arithmetic average of the cumulative distributions for the individual observations. Often, the interest is in PX sub 1 x sub 1, X sub n or x sub n for practical applications. An approximate expression, also sharp upper and lower bounds, are developed for PX sub 1 x sub 1, X sub n or x sub n in terms of n and F bar x sub nn - F bar x sub 1n. Author
- Statistics and Probability