Mixture representations of noncentral distributions
| Autor: | Ludwig Baringhaus, Rudolf Grübel |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
021103 operations research Probability (math.PR) Mathematical analysis 0211 other engineering and technologies Mathematics - Statistics Theory Statistics Theory (math.ST) 02 engineering and technology 01 natural sciences Symmetric probability distribution 010104 statistics & probability Primary 62E10 secondary 60E05 FOS: Mathematics Mixture distribution 0101 mathematics Parametric family Random variable Real line Mathematics - Probability Mathematics |
| 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: | OpenAIRE |
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