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- W3128889633 abstract "The Poisson-Kingman distributions, $mathrm{PK}(rho)$, on the infinite simplex, can be constructed from a Poisson point process having intensity density $rho$ or by taking the ranked jumps up till a specified time of a subordinator with L'evy density $rho$, as proportions of the subordinator. As a natural extension, we replace the Poisson point process with a negative binomial point process having parameter $r>0$ and L'evy density $rho$, thereby defining a new class $mathrm{PK}^{(r)}(rho)$ of distributions on the infinite simplex. The new class contains the two-parameter generalisation $mathrm{PD}(alpha, theta)$ of Pitman and Yor (1997) when $theta>0$. It also contains a class of distributions derived from the trimmed stable subordinator. We derive properties of the new distributions, with particular reference to the two most well-known $mathrm{PK}$ distributions: the Poisson-Dirichlet distribution $mathrm{PK}(rho_theta)$ generated by a Gamma process with L'evy density $rho_theta(x) = theta e^{-x}/x$, $x>0$, $theta > 0$, and the random discrete distribution, $mathrm{PD}(alpha,0)$, derived from an $alpha$-stable subordinator." @default.
- W3128889633 created "2021-02-15" @default.
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- W3128889633 date "2017-01-01" @default.
- W3128889633 modified "2023-10-06" @default.
- W3128889633 title "Negative Binomial Construction of Random Discrete Distributions on the Infinite Simplex" @default.
- W3128889633 hasPublicationYear "2017" @default.
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