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• W2017451286 abstract "Using and refining a technique developed by O. Thorin, we prove: THEOREM. Let $f(x) = Ccdot x^{beta - 1} h(x), x > 0$, be a probability density on $(0, infty)$. Here $beta > 0$ and $h$ is continuous and satisfies $h(0) = 1$. Assume that $h$ can be analytically continued to the whole complex plane cut along the negative real axis and assume that $h$ satisfies some other regularity assumptions. If $h$ is completely monotone on $(0, infty)$ and if, for each fixed $u > 0$, the function $h(unu(t))h(u/nu(t))$, where $nu(t) = t + 1 + (t^2 + 2t)^{frac{1}{2}}$, is completely monotone on $(0, infty)$, then $f(x)$ is the density of a generalized gamma convolution and hence infinitely divisible. The theorem is applied to show the infinite divisibility of a rather large class of probability densities on $(0, infty)$. In particular we show that a power with exponent of modulus $geqslant 1$ of the ratio of two gamma distributed rv's has an infinitely divisible distribution." @default.
• W2017451286 created "2016-06-24" @default.
• W2017451286 creator A5056325791 @default.
• W2017451286 date "1979-12-01" @default.
• W2017451286 modified "2023-10-18" @default.
• W2017451286 title "A General Result on Infinite Divisibility" @default.
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• W2017451286 doi "https://doi.org/10.1214/aop/1176994890" @default.
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