A Method for Deriving Probability Distributions with Gamma Functions,

Abstract

Based on an exponential integral formula recently derived by the authors, a substitution method is presented for determining a probability density function and moments for a useful class of (0, infinity) exponentials frequently encountered in signal processing. The generalization of the method is elaborated to account for models of (-infinity, infinity) exponentials. The generalized density function and moments relation are given as integral formulas specifically calculated from their definitions in probability theory. Several examples of the method are provided, including an example for modeling random signals and deterministic acoustic signals in underwater acoustics. The generalization of the method for multivariate distributions is presented. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Jan 16, 1996
Accession Number
ADA306245

Entities

People

  • B. J. Bates
  • F. J. O'brien Jr.
  • T. Nguyen Chien

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Acoustic Signals
  • Complex Variables
  • Data Analysis
  • Data Science
  • Exponential Functions
  • Information Processing
  • Information Science
  • Integrals
  • Mathematics
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Regression Analysis
  • Signal Processing
  • Statistics
  • Underwater Acoustics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.