Jones, M. C.
The complementary beta distribution.
Journal of Statistical Planning and Inference, 104(2),
The complementary beta distribution is proposed as a new distribution on the unit interval. It results from reversing the roles of the distribution and quantile functions of the beta distribution. It has some attractive properties that are complementary to those of the beta distribution. In particular, the complementary beta distribution is much more amenable than the beta distribution to exact computations involving expectations of order statistics, including L-moments. At least for a wide range of parameter values, complementary beta and beta distributions with parameters that are reciprocals of the other's parameters are good approximations to one another. We also note the position of the complementary beta distribution in a wider family of distributions defined through the same simple form for their quantile density functions.
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