The Open UniversitySkip to content

The complementary beta distribution

Jones, M. C. (2002). The complementary beta distribution. Journal of Statistical Planning and Inference, 104(2) pp. 329–337.

DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


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.

Item Type: Journal Item
Copyright Holders: 2002 Elsevier Science B.V.
ISSN: 0378-3758
Keywords: beta distribution; L-moments; order statistics; quantile density function; quantile function
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 22666
Depositing User: Sarah Frain
Date Deposited: 10 Aug 2010 11:59
Last Modified: 07 Dec 2018 09:38
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU