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Inequalities for quantiles of the chi-square distribution. (English) Zbl 1231.62092
Summary: We obtain a new sharp lower estimate for tails of the central chi-square distribution. Using it we prove quite accurate lower bounds for the chi-square quantiles covering the case of increasing number of degrees of freedom and simultaneously tending to zero tail probabilities. In the case of small tail probabilities we also provide upper bounds for these quantiles which are close enough to the lower ones. As a byproduct we propose a simple approximation formula which is easy to calculate for the chi-square quantiles. It is expressed explicitly in terms of tail probabilities and a number of degrees of freedom.

MSC:
62G32 Statistics of extreme values; tail inference
62E15 Exact distribution theory in statistics
62E17 Approximations to statistical distributions (nonasymptotic)
60E15 Inequalities; stochastic orderings
65C60 Computational problems in statistics (MSC2010)
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