On univariate and bivariate generalized gamma convolutions |
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Authors: | Lennart Bondesson |
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Institution: | aDepartment of Mathematics and Mathematical Statistics, Umeå University, SE-90187 Umeå, Sweden |
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Abstract: | This paper has two parts. In the first part some results for generalized gamma convolutions (GGCs) are reviewed. A GGC is a limit distribution for sums of independent gamma variables. In the second part, bivariate gamma distributions and bivariate GGCs are considered. New bivariate gamma distributions are derived from shot-noise models. The remarkable property hyperbolic complete monotonicity (HCM) for a function is considered both in the univariate case and in the bivariate case. |
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Keywords: | Bivariate gamma distribution Generalized gamma convolution Hyperbolic complete monotonicity (HCM) Shot-noise models |
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