Accession Number : AD0648045

Title :   ASYMPTOTIC VARIANCES AND COVARIANCES OF MAXIMUM-LIKELIHOOD ESTIMATORS, FROM CENSORED SAMPLES, OF THE PARAMETERS OF A FOUR-PARAMETER GENERALIZED GAMMA POPULATION.

Descriptive Note : Internal rept.,

Corporate Author : AEROSPACE RESEARCH LABS OFFICE OF AEROSPACE RESEARCH WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Harter,H. Leon

Report Date : AUG 1966

Pagination or Media Count : 155

Abstract : Just how applicable the asymptotic variances and covariances are to estimates from samples of small or even moderate size is an open question. Conceptually, this question might be settled by a Monte Carlo study, but from a practical standpoint, any such study large enough to be conclusive would be ruled out by the excessive machine time required. Results of a small Monte Carlo study for the three-parameter Weibull population, reported by Harter and Moore, indicate that when three (or more) parameters, including the location parameter c, are being estimated simultaneously, the variances and the absolute values of the covariances are substantially in excess of the values given by the asymptotic formulas, even for sample size n as large as 100. The excess, however, appears to be proportional to n to the -2 and hence, for sufficiently large n, becomes negligible in comparison with the values given by the asymptotic formulas, which are proportional to n to the -1. (Author)

Descriptors :   (*ANALYSIS OF VARIANCE, *STATISTICAL DISTRIBUTIONS), SAMPLING, POPULATION(MATHEMATICS), MONTE CARLO METHOD, PROBABILITY DENSITY FUNCTIONS, MATRICES(MATHEMATICS)

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE