A Method for Deriving Probability Distributions with Gamma Functions,

O'Brien, F. J; Jr.; Nguyen, C. T.; Bates, B. J.

A Method for Deriving Probability Distributions with Gamma Functions,

1996

O'Brien, F. J | Jr. | Nguyen, C. T. | Bates, B. J.

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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AGROVOC Keywords

analysis of variance integral equations least squares method mathematical models regression analysis statistical data stochastic processes time series analysis

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Other Subjects

Hypotheses; Special functions(mathematics); Statistics and probability; Random variables; Normalizing(statistics); Acoustic signals; *probability density functions; *multivariate analysis; Probability distribution functions; Underwater acoustics; Exponential functions; Chi square test; Method of moments; *signal processing; Gamma functions; Formulas(mathematics); Normal distribution.

Language

English

License

http://handle.dtic.mil/100.2/ADA306245APPROVED FOR PUBLIC RELEASE

Source

NAVAL UNDERSEA WARFARE CENTER NEWPORT DIV RIDTIC AND NTIS

Corporate Author

NAVAL UNDERSEA WARFARE CENTER NEWPORT DIV RI

In AGRIS since: 2013-06-15

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A Method for Deriving Probability Distributions with Gamma Functions,

1996

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