GENERAL RENEWAL ANALYSIS,

Abstract

The report describes a general procedure for finding an approximation to the n th order failure distribution using orthogonal polynomials. Applications are found in renewal analysis. The method requires knowledge of only the statistical moments of the primary failure distribution. As an illustration of the accuracy of the approximation, the exponential distribution and its first six convolutions are approximated by Laguerre polynomials and compared with the actual probability density functions--gamma functions, in this case. The case of the log-normal distribution is also worked out for a selected set of population parameters. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1967
Accession Number
AD0648182

Entities

People

  • George Schlenker

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Convolution
  • Data Science
  • Functions (Mathematics)
  • Information Science
  • Mathematical Analysis
  • Mathematics
  • Normal Distribution
  • Polynomials
  • Probability
  • Probability Density Functions
  • Random Variables

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.