Work

On the Cumulative Distribution Function of the Difference of Two Dependent Chi Square Random Variables

Year: 2025

Type: article

Abstract: In this article, we reexamine the derivation of the cumulative distribution function of the difference of two dependent chi-square random variables with the same degrees of freedom. We derive the cdf for this difference for even degrees of freedom and discuss a discrepancy that we have found with a reported cdf of this difference for even degrees of freedom in [6]. For odd degrees of freedom, an expression for the cdf seems to be unknown. In this case, we derive a representation of the cdf in terms of the Meijer G-function. These representations allowed us to compute percentiles for even and odd degrees of freedom.

Source: European Journal of Mathematical Analysis

DOI: 10.28924/ada/ma.5.19

Authors: Elias G. Saleeby, Anwar H. Joarder, Nima Rabiei

Institutions: Al Akhawayn University, International University of Sarajevo

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4412891981

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Related to: 10