Abstract
Random distribution functions are the basic tool for solving nonparametric decision-theoretic problems. In 1974, Doksum introduced the family of distributions neutral to the right, that is, distributions such thatF(t 1),[F(t 2)−F(t 1)]/[1 −F(t 1)],...,[F(t k)−F(t k − 1)]/[1 −F(t k − 1)] are independent whenevert 1 < ... <t kIn practice, application of distributions neutral to the right has been prevented by the lack of a manageable analytical expression for probabilities of the typeP(F(t)<q) for fixedt andq. A subclass of such distributions can be provided which allows for a close expression of the characteristic function of log[1−F(t)], given the sample. Then, thea posteriori distribution ofF(t) is obtained by numerical evaluation of a Fourier integral. As an application, the global optimization problem is formulated as a problem of inference about the quantiles of the distributionF(y) of the random variableY=f(X), wheref is the objective function andX is a random point in the search domain.
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Communicated by L. C. W. Dixon
The author thanks J. Koronacki and R. Zielinski of the Polish Academy of Sciences for their valuable criticism during the final draft of the paper.
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Betro, B. Bayesian testing of nonparametric hypotheses and its application to global optimization. J Optim Theory Appl 42, 31–50 (1984). https://doi.org/10.1007/BF00934132
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DOI: https://doi.org/10.1007/BF00934132