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Families of complementary distributions

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  • Jones, M.C.

Abstract

Each continuous distribution on (0,1), with cumulative distribution function F say, has a complementary distribution which is the distribution with cumulative distribution function F−1. Some basic general properties of complementary distributions are given.A particular focus of this article is then the construction of families of distributions, each based on a given F and indexed by a single additional parameter, which are closed under complementarity; properties of these families of distributions are explored, as are those of a particular special case.

Suggested Citation

  • Jones, M.C., 2018. "Families of complementary distributions," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 74-81.
    • Handle: RePEc:eee:stapro:v:141:y:2018:i:c:p:74-81
    DOI: 10.1016/j.spl.2018.05.021
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    References listed on IDEAS

    as
    1. M. C. Jones & Arthur Pewsey, 2012. "Inverse Batschelet Distributions for Circular Data," Biometrics, The International Biometric Society, vol. 68(1), pages 183-193, March.
    2. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
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