Accession Number : ADA115491

Title :   Nonparametric Estimation of Distribution and Density Functions with Applications.

Descriptive Note : Doctoral thesis,

Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING

Personal Author(s) : Sweeder,James

PDF Url : ADA115491

Report Date : May 1982

Pagination or Media Count : 275

Abstract : This report presents the theoretical development, evaluation, and applications of a new nonparametric family of continuous, differentiable, sample distribution functions. Given a random sample of independent, identically distributed random variables, estimators are constructed which converge uniformly to the underlying distribution. A smoothing routine is proposed which preserves the distribution function properties of the estimators. Using mean integrated square error as a criterion, the new estimators are shown to compare favorably against the empirical distribution function. As density estimators, their derivatives are shown to be competitive with other continuous approximations. Numerous graphical examples are given. New goodness of fit tests for the normal and extreme value distributions are proposed based on the new estimators. Eight new goodness of fit statistics are developed. Extensive Monte Carlo studies are conducted to determine the critical values and powers for tests when the null hypothesis is completely specified and when the parameters of the null hypothesis are estimated. These tests were shown to be comparable with or superior to tests currently used. (Author)

Descriptors :   *NONPARAMETRIC STATISTICS, DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, PROBABILITY DENSITY FUNCTIONS, NORMAL DISTRIBUTION, MONTE CARLO METHOD, THESES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE