Compound gamma,beta and F distributions |
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Authors: | Satya D Dubey |
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Institution: | (1) New York University, 10453 New York, N. Y., U.S.A. |
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Abstract: | Summary In this paper a compound gamma distribution has been derived by compounding a gamma distribution with another gamma distribution.
The resulting compound gamma distribution has been reduced to the Beta distributions of the first kind and the second kind
and to theF distribution by suitable transformations. This includes theLomax distribution as a special case which enjoys a useful property. Moment estimators for two of its parameters are explicitly
obtained, which tend to a bivariate normal distribution. The paper contains expressions for a bivariate probability density
function, its conditional expectation, conditional variance and the product moment correlation coefficient. Finally, all the
parameters of the compound gamma distribution are explicitly expressed in terms of the functions of the moments of the functions
of random variables in two different ways.
This note is based on a technical report prepared by the author while he was with the Procter and Gamble Company. |
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