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A distribution F is less dispersed than a distribution G if for all . We generalize a characterization of dispersive ordering of Shaked (1982) concerning sign changes of Fc – G, where Fc is a translate of F. We then use this generalization plus total positivity to develop a simple proof of a characterization of dispersive distributions due to Lewis and Thompson (1981); a distribution H is dispersive if
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Lynch et al. (1983) studied this question.
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