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Abstract:
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Given a lifetime distribution function W(x), another lifetime distribution may be generated through a proportional odds transformation W(x; t) = W(x)/(W(x) + t(1 - W(x)), where t > 0. It is shown that the p.o. transformation partitions the set of all lifetime distributions. In each equivalence class, all members are related through p.o. transformations. Within each class, there is a stochastic ordering of distributions according to t, with dispersion of the transformed distribution being a strictly increasing function of t. Conditions for the existence of moments and moment-generating functions are established; it is shown that either every member of a class has a m.g.f., or none does. It is also shown that the Kullback-Leibler information function for two distributions related by a proportional odds transformation is a strictly increasing function of t, for t > 1.
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