An Alternative Proof for the Difference of Two Non-central Chi-square Quadratic Polynomials to be Non-central Chi-square

Phil D. Young and Dean M. Young

International Journal of Statistics and Probability, 2025, vol. 13, issue 2, 66

Abstract: Baksalary and Kala (1980) and Baksalary and Kala (1983) have provided necessary and sufficient conditions for the difference of two quadratic polynomial random variables defined from same multivariate normal distribution, and each having a non-central chi-square distribution, to have a non-central chi-square distribution. Here, we give a somewhat simpler alternative characterization to that in Proposition 1 in Baksalary and Kala (1980).

Date: 2025
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