A (non‐central) chi‐squared mixture of non‐central chi‐squareds is (non‐central) chi‐squared and related results, corollaries and applications. Issue 1 (11th August 2021)

• Record Type: Journal Article
• Authors: Jones, M. C.; Marchand, Éric
• Is Part Of: Stat. Volume 10:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-08-11
• Subjects: beta distribution -- binomial mixture -- F distribution -- gamma distribution -- Libby–Novick distribution -- negative binomial mixture; Statistics -- Periodicals; 519.2
• DOI: 10.1002/sta4.398
• Languages: English
• ISSNs: 2049-1573

Abstract

Abstract : Our main, novel, result is that a certain non‐central chi‐squared mixture of non‐central chi‐squared distributions is itself a scaled non‐central chi‐squared distribution. From this and a link to a known result on a mixture representation for a scaled central chi‐squared distribution, numerous further mixture results, both old and new, ensue. These include mixture results for central F, non‐central F and Libby–Novick distributions. The main result involves distributions all with the same degrees of freedom; it is also extended to the case where the mixing non‐central chi‐squared distribution has degrees of freedom an even number larger than that of the conditional non‐central chi‐squared distribution, with further consequences pursued.