Accession Number : ADA306245

Title :   A Method for Deriving Probability Distributions with Gamma Functions,

Corporate Author : NAVAL UNDERSEA WARFARE CENTER NEWPORT DIV RI

Personal Author(s) : O'Brien, F. J., Jr. ; Nguyen, C. T. ; Bates, B. J.

PDF Url : ADA306245

Report Date : 16 JAN 1996

Pagination or Media Count : 37

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)

Descriptors :   *SIGNAL PROCESSING, *MULTIVARIATE ANALYSIS, *PROBABILITY DENSITY FUNCTIONS, MATHEMATICAL MODELS, STOCHASTIC PROCESSES, PROBABILITY DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, STATISTICAL DATA, TIME SERIES ANALYSIS, ANALYSIS OF VARIANCE, REGRESSION ANALYSIS, LEAST SQUARES METHOD, ACOUSTIC SIGNALS, HYPOTHESES, NORMALIZING(STATISTICS), EXPONENTIAL FUNCTIONS, METHOD OF MOMENTS, INTEGRAL EQUATIONS, UNDERWATER ACOUSTICS, SPECIAL FUNCTIONS(MATHEMATICS), CHI SQUARE TEST, FORMULAS(MATHEMATICS), NORMAL DISTRIBUTION.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE