The complementary beta distribution |
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| Institution: | 1. GREThA UMR-CNRS 5113, Université de Bordeaux, France;2. ECREB, West University of Timisoara, Romania;1. Academy of Mathematics and Statistics, Hubei engineering University, China;2. Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, China;3. School of Statistics, Capital University of Economics and Finance, China;4. School of Mathematics and Statistics, University of Science and Technology of China, China;1. College of Basic Science, Tianjin Agricultural University, Tianjin 300384, China;2. School of Business, Ningbo University, Ningbo 315211, China;3. College of Computer and Information, Zhejiang Wanli University, Ningbo 315100, China;4. Lithuanian Institute of Agrarian Economics, V. Kudirkos Str. 18/2, LT-03105 Vilnius, Lithuania;1. Physics Department, North Bengal University, Siliguri 734013, India;2. Computer and Information Sciences Department, SUNY, Fredonia, NY 14063, United States |
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| Abstract: | 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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