Accession Number : AD0672954

Title :   CONSTRAINED MAXIMUM LIKELIHOOD ESTIMATION OF N STOCHASTICALLY ORDERED DISTRIBUTIONS,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Geoffrion,A. M.

Report Date : JUL 1968

Pagination or Media Count : 41

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
      Mfg & Industrial Eng & Control of Product Sys

Distribution Statement : APPROVED FOR PUBLIC RELEASE