ON MAXIMUM LIKELIHOOD ESTIMATORS OF SHAPE AND SCALE PARAMETERS AND THEIR APPLICATION IN CONSTRUCTING CONFIDENCE CONTOURS

Abstract

In a paper by Thoman, Baine and Antle, it was shown that certain pivotal functions of the maximum likelihood estimators for parameters in the Weibull family have distributions which are parameter-free. By using Monte Carlo methods, this basic result made possible the production of tables of the percentile points of these distributions so that confidence intervals for the parameters can be determined. In turn this makes possible tests of hypotheses regarding the parameters. It is the purpose of this note to generalize this result in several respects. Firstly, to point out that for any given continuous distribution with support on the positive line and unknown shape and scale parameters the same pivotal functions of the maximum likelihood estimators are parameter-free. Secondly, that the same conclusion holds for incomplete samples censored under certain conditions or terminated at a given ordered observation.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1970
Accession Number
AD0708811

Entities

People

  • Sam C. Saunders

Organizations

  • Boeing

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Data Science
  • Distribution Functions
  • Equations
  • Estimators
  • Fatigue Tests (Mechanics)
  • Generators
  • Information Science
  • Intervals
  • Monte Carlo Method
  • Normal Distribution
  • Probability
  • Random Number Generators
  • Random Variables
  • Sampling
  • Statistical Sampling
  • Statistical Tests
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Statistical inference.