Accession Number : AD0702518

Title :   FURTHER RESULTS ON ESTIMATION OF THE PARAMETERS OF THE PEARSON TYPE III AND WEIBULL DISTRIBUTIONS IN THE NONREGULAR CASE,

Corporate Author : C-E-I-R INC BEVERLY HILLS CALIF

Personal Author(s) : Blischke,W. R. ; Mundle,P. B. ; Johns,M. V. , Jr. ; Truelove,A. J.

Report Date : NOV 1968

Pagination or Media Count : 98

Abstract : The report is the third in a series of ARL Technical Documentary Reports on the subject on non-regular estimation. The first of these covered research on the construction of a non-trivial lower bound on the variance of unbiased estimators of the location parameter of the Pearson Type 3 and other distributions in the non-regular case. The second included the results of a numerical investigation of the bound for the Type 3 distribution and some analytical results on exact and approximate Pitman estimators. Further analytical results are discussed in this report. Approximations based on linear combinations of order statistics and on powers of order statistics are found to have asymptotic variances of the same order of magnitude. Some recent analytical results indicate that this is the best order attainable. Some comments on the estimation problem in the'regular' case are also included. Certain of the analytical results are extended to the Weibull distribution. Numerical studies have also been undertaken. The results confirm the theoretical conclusion that the variances of the approximate and exact Pitman estimators are of the same order of magnitude and the numerical results that the variance bounds are of this order as the sample size increases. Numerical results concerning a joint estimator based on the Pitman estimator of the location parameter and the maximum likelihood estimators of the shape and scale parameters are also included. This procedure is found to be unacceptable except for large sample sizes. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, DECISION THEORY), PROBABILITY DENSITY FUNCTIONS, ANALYSIS OF VARIANCE, SAMPLING

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE