Accession Number : ADA116361

Title :   On Approximation of the Level Probabilities and Associated Distributions in Order Restricted Inference.

Descriptive Note : Technical rept.,


Personal Author(s) : Robertson,Tim ; Wright,F T

PDF Url : ADA116361

Report Date : 17 Jun 1982

Pagination or Media Count : 37

Abstract : The use of the distribution theory developed for order restricted inference has been limited by the lack of computation algorithms for the 'level probabilities' encountered in that theory. An approximation for these level probabilities, which accounts for the pattern of large and small 'weights,' is developed. This approximation and the equal weights approximation are examined in several different ways including the use of randomly generated weight sets. Both approximations appear to be reasonable for weight sets having a moderate amount of variability. The quality of the equal weights approximation, as a function of the amount of variability in the weights, deteriorates more quickly for certain patterns of large and small weights than for others. Thus, the approximation based upon the pattern of large and small weights is a significant improvement over the equal weights approximation. Finally, Siskind's (1976) approximation, which can be applied if the number of parameters is not too large, is discussed. (Author)

Descriptors :   *Order statistics, *Probability distribution functions, *Approximation(Mathematics), *Distribution theory, Computations, Algorithms, Statistical inference, Regression analysis, Variables, Chi square test, Weighting functions, Deterioration, Parameters

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE