Abstract
A decision maker is interested in a quantity θ. He consults an expert who provides three fractiles of her probability distribution for θ. The problem discussed in this paper is how the decision maker should use the expert's fractiles to produce his distribution for θ. A key ingredient has to be the decision maker's opinion of the expert. Our analysis shows how the Bayesian approach clearly incorporates this feature. With three fractiles provided, information about the skewness of the distribution of θ is available, in addition to location and scale. Our development uses the skew logistic to accommodate this additional feature, and much of the paper is concerned with skewness, extending the methods of Lindley for the symmetric case. The ideas easily extend to several experts if the unrealistic assumption is made that the decision maker regards them as independent.
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