Families of Complementary Distributions

Jones, M. C. (2018). Families of Complementary Distributions. Statistics & Probability Letters, 141 pp. 74–81.

DOI: https://doi.org/10.1016/j.spl.2018.05.021

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.

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