Use of the Maximum Likelihood Method under Quantal Responses for Estimating the Parameters of a Normal Distribution and Its Application to an Armor Penetration Problem

Abstract

Necessary and sufficient conditions are obtained for the existence of the maximum likelihood estimates (MLE) of the parameters of a normal distribution for quantal responses. It is shown that whenever the MLE estimates exist they are unique. A modified Newton-Raphson procedure is given which will converge globally to the MLE estimates. These results are new and directly applicable to an armor plate penetration problem or any other types of experiments based on quantal responses which fall under a normal distribution. A computer program is described which includes as output a set of plotted confidence ellipses centered about the MLE. Various examples and the corresponding computer outputs are given. Probit analysis and confidence regions for small samples are discussed in separate appendices. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1972
Accession Number
AD0762399

Entities

People

  • A. R. Didonato
  • M. P. Jarnagin Jr.

Organizations

  • Naval Surface Warfare Center Dahlgren Division

Tags

Communities of Interest

  • Air Platforms
  • Biomedical
  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Asymptotic Series
  • Computations
  • Computer Programs
  • Data Science
  • Factor Analysis
  • Information Science
  • Machine Languages
  • Mathematical Analysis
  • Numerical Analysis
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Real Numbers
  • Statistical Algorithms
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.
  • ballistics.