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Bounds for non-central chi-square distributions having unobservable random non-centrality parameters

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  • Szroeter, Jerzy

Abstract

Let X be a random variate whose distribution conditional on an unobservable variate Y is chi-square with s degrees of freedom and non-centrality parameter equal to Y. Upper and lower bounds for the unconditional d.f. of X are derived when only the values of location and randomness indices for Y are known. The numerical quality of the bounds is illustrated for a range of parameter values. An application to testing hypotheses in random coefficients regression models is presented.

Suggested Citation

  • Szroeter, Jerzy, 1992. "Bounds for non-central chi-square distributions having unobservable random non-centrality parameters," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 73-81, January.
    • Handle: RePEc:eee:stapro:v:13:y:1992:i:1:p:73-81
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