APPROXIMATE JOINT PROBABILITIES FOR LARGEST AND SMALLEST OF A SET OF INDEPENDENT OBSERVATIONS.
Abstract
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 (x;n) be the arithmetic average of the cumulative distributions for the individual observations. Often, the interest is in P(X 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 P(X sub 1 > x sub 1, X sub n = or < x sub n) in terms of n and F bar (x sub n;n) - F bar (x sub 1;n). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 13, 1968
- Accession Number
- AD0679680
Entities
People
- John E. Walsh
Organizations
- Southern Methodist University