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An inequality for a class of bivariate chi-square distributions. (English) Zbl 0175.17306
Summary: The inequality \[ \text{Pr}\{c_1\leq U_1\leq c_2,\;c_1\leq U_2\leq c_2\}\geq \text{Pr}\{c_1\leq U_1\leq c_2\}\times\text{Pr}\{c_1\leq U_2\leq c_2\} \] is shown to hold when the joint distribution of \(U_1\) and \(U_2\) is a member of a class of bivariate chi-square distributions given. The relevance of this result to the construction of two-sided simultaneous confidence intervals for variances is noted.

MSC:
62-XX Statistics
Keywords:
statistics
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