summary Exact expressions for the distribution function of a random variable of the form c1χ2m+c2χ2n are given where χ2m and χ2nχ2n are independent chi‐square random variables with m and n degrees of freedom respectively. (The positive ci are distinct). In particular, the exact asymptotic distribution function for the average Kendall tau statistic is written as a function of tables of Solomon (1960) and some found in Abramowitz and Stegun's Handbook of Mathematical Functions.
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Bock et al. (1988) studied this question.
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