SCALE PARAMETER ESTIMATION OF THE GAMMA PROBABILITY FUNCTION BASED ON ONE ORDER STATISTIC,

Abstract

An unbiased maximum likelihood estimator for the scale parameter of the parent Gamma probability density function (shape parameter known) is developed, based on one order statistic. Three tables are produced. Tabe I contains the value of the mth smallest order statistic maximizing the efficiency of the estimator (as compared with the minimum variance unbiased estimator) for sample sizes n=1 to 50 by steps of 1. Table II contains coefficients of the mth order statistic of sample size n from the Gamma probability density function in exact upper and lower confidence bounds for the scale parameter. The mth smallest order statistic maximizing the efficiency of the upper bound is tabulated and if this value of m is not the same as that for the order statistic maximizing the efficiency of the central confidence interval the mth smallest order statistic maximizing the efficiency of the central confidence interval is tabulated in table III. Table values for a shape parameter of one were checked for accuracy against published results and agreed to within one digit in the last place. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1963
Accession Number
AD0425223

Entities

People

  • Robert Clay Karns

Organizations

  • Air Force Institute of Technology

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Coefficients
  • Data Science
  • Efficiency
  • Estimators
  • Information Science
  • Intervals
  • Mathematics
  • Probability
  • Probability Density Functions
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Statistical inference.