Accession Number : AD0688404

Title :   ESTIMATING THE PARAMETER k OF THE RAYLEIGH DISTRIBUTION FROM CENSORED SAMPLES.

Descriptive Note : Master's thesis,

Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

Personal Author(s) : Brock,Dwight B.

Report Date : 16 APR 1969

Pagination or Media Count : 28

Abstract : Let g(x) be the ratio of the ordinate and the probability integral for the Rayleigh distribution. That is, g(x) = f(x)/F(x), where f(x) = (2x/k)exp(-x squared/k), x > 0, k > 0, and F(x) = the integral from 0 to x of f(t)dt. Tiku's local approximation g(x) is approximately equal to alpha + beta x/the square root of k is used to simplify the maximum likelihood equation for estimating k from a doubly censored sample from this population. The solution to the simplified maximum likelihood equation is the estimator for k, which is called k sub c. It is much easier to compute than the maximum likelihood estimator, since no iterative procedure is required. After the solution for k sub c is given, equations are developed for its bias and variance. Numerical comparisons are made among k sub c and other estimators for k. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, DECISION THEORY), DISTRIBUTION THEORY, EXPONENTIAL FUNCTIONS, ANALYSIS OF VARIANCE, LEAST SQUARES METHOD, SAMPLING, THESES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE