Mixture representations of noncentral distributions

Ludwig Baringhaus and Rudolf Grübel

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 24, 5997-6013

Abstract: With any symmetric distribution μ on the real line we may associate a parametric family of noncentral distributions as the distributions of (X+δ)2,δ=0, where X is a random variable with distribution μ. The classical case arises if μ 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.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2020.1738487 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:50:y:2021:i:24:p:5997-6013

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2020.1738487

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().