On Mixtures of Distributions: A Survey and Some New Results on Ranking and Selection

Abstract

This paper surveys some of the literature dealing with mixtures of distributions. The topics covered relate to probabilistic properties, estimation, hypotheses testing and multiple decision (selection and ranking) procedures. The results reviewed concerning probabilistic properties of mixture distributions include the identifiability, scale mixture, infinite divisibility, atomicity and perfectness. The results on estimation theory reviewed include the method of moments, method of maximum likelihood estimation, method of least squares, Bayesian estimation, and the method of curve fitting. The results for hypotheses testing provide tests for hypothesis whether an observed sample is a mixture from two samples with certain unknown proportion and also provide test if the mean of the mixture population is equal to some known value. In the last section, we give some new results for selection and ranking procedures for mixtures of distributions.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1979
Accession Number
ADA077635

Entities

People

  • Shanti Gupta
  • Wen-tao Huang

Organizations

  • Purdue University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Artificial Intelligence
  • Computational Science
  • Computations
  • Data Science
  • Discrete Distribution
  • Distribution Functions
  • Estimators
  • Information Science
  • Maximum Likelihood Estimation
  • Monte Carlo Method
  • Normal Distribution
  • Observation
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Surveys
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.

Technology Areas

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