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Some properties of bivariate Gumbel Type A distributions with proportional hazard rates

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  • Elandt-Johnson, Regina C.

Abstract

We call a set of univariate distributions with the same mathematical form but different parameter values a family . Consider a bivariate Gumbel Type A survival distribution, S12(x1, x2), defined in (2.1), for which both marginal distributions, S1(x1), S2(x2), belong to the same family, of distributions. It is proved in this paper that subject to weak conditions, the crude hazard rates, h1(t) and h2(t), are proportional if and only if the marginal hazard rates, [lambda]1(t) and [lambda]2(t), are proportional (Theorem 1). It is also shown that the survival functions of W = min(X1, X2), and of the identified minimum, Wi = Xi, for Xi

Suggested Citation

  • Elandt-Johnson, Regina C., 1978. "Some properties of bivariate Gumbel Type A distributions with proportional hazard rates," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 244-254, June.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:2:p:244-254
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    Cited by:

    1. Roy, Dilip & Mukherjee, S. P., 1998. "Multivariate Extensions of Univariate Life Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 72-79, October.

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