A (Non‐Central) Chi‐Squared Mixture of Non‐Central Chi‐Squareds is (Non‐Central) Chi‐Squared, and Related Results, Corollaries and Applications

Jones, M. C. and Marchand, Éric (2021). A (Non‐Central) Chi‐Squared Mixture of Non‐Central Chi‐Squareds is (Non‐Central) Chi‐Squared, and Related Results, Corollaries and Applications. Stat, 10(1), article no. e398.

DOI: https://doi.org/10.1002/sta4.398

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.

Viewing alternatives

Download history

Metrics

Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions

Export

About

Recommendations