Maximum Likelihood Estimation and Hypothesis Testing in the Bivariate Exponential Model of Marshall and Olkin.

Abstract

The present work concerns statistical inference in the bivariate exponential distribution introduced by Marshall and Olkin. Even though the distribution has a singular component, the use of a special dominating measure leads to an explicit form of the likelihood whose properties are investigated. The existence, uniqueness and asymptotic distributional properties of the maximum likelihood estimators are studied. Using the criterion of generalized variance, it is shown that the simple unbiased estimators proposed by Arnold are asymptotically less efficient than the maximum likelihood estimators and the loss in efficiency is particularly serious in the case of independence. Uniformly most powerful test for independence is derived for the special model having identical marginal distributions.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1971
Accession Number
AD0737530

Entities

People

  • G. K. Bhattacharyya
  • Richard A. Johnson

Organizations

  • University of Wisconsin Madison Department of Statistics

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Asymptotic Normality
  • Data Science
  • Efficiency
  • Equations
  • Estimators
  • Information Science
  • Maximum Likelihood Estimation
  • Normal Distribution
  • Probability
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistical Samples
  • Statistics
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms