Accession Number:

AD0672954

Title:

CONSTRAINED MAXIMUM LIKELIHOOD ESTIMATION OF N STOCHASTICALLY ORDERED DISTRIBUTIONS,

Descriptive Note:

Corporate Author:

RAND CORP SANTA MONICA CALIF

Personal Author(s):

• Geoffrion,A. M.

Report Date:

1968-07-01

Pagination or Media Count:

41.0

Abstract:

A consideration is made of the problem of determining step function maximum likelihood estimates for N stochastically ordered distributions, subject to the constraint that the estimates themselves must also be stochastically ordered. Brunk and others achieved a closed form solution for the case where N equals 2, but they were unable to extend the results to the case where N is greater than 2. This study presents a new analytical method based on the Kuhn-Tucker optimality conditions for the equivalent concave program. For N equal to 2, the method yields the closed form solution of Brunk. When used in conjunction with a reduction strategy previously developed by the author, the method yields an efficient computational algorithm for N equal to or greater than three. Computational experience shows that large problems can be solved in reasonable time with good accuracy, especially when compared with the performance of a general nonlinear programming algorithm applied directly to the equivalent concave program. Author

Descriptors:

• (*STATISTICAL ANALYSIS
• RELIABILITY)
• STATISTICAL DISTRIBUTIONS
• STATISTICAL PROCESSES
• STOCHASTIC PROCESSES
• MATHEMATICAL PROGRAMMING
• PROBLEM SOLVING
• OPTIMIZATION
• ALGORITHMS
• THEOREMS

Subject Categories:

• Operations Research
• Manufacturing and Industrial Engineering and Control of Production Systems

Distribution Statement:

APPROVED FOR PUBLIC RELEASE