| Autor: |
Baringhaus, Ludwig, Grübel, Rudolf |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Commun. Stat., Theory Methods 50, No. 24, 5997-6013 (2021) |
| Druh dokumentu: |
Working Paper |
| Popis: |
With any symmetric distribution $\mu$ on the real line we may associate a parametric family of noncentral distributions as the distributions of $(X+\delta)^2$, $\delta\not=0$, where $X$ is a random variable with distribution $\mu$. The classical case arises if $\mu$ is the standard normal distribution, leading to the noncentral chi-squared distributions. It is well-known that these may be written as Poisson mixtures of the central chi-squared distributions with odd degrees of freedom. We obtain such mixture representations for the logistic distribution and for the hyperbolic secant distribution. We also derive alternative representations for chi-squared distributions and relate these to representations of the Poisson family. While such questions originated in parametric statistics they also appear in the context of the generalized second Ray-Knight theorem, which connects Gaussian processes and local times of Markov processes. |
| Databáze: |
arXiv |
| Externí odkaz: |
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