Beta trigonometric distributions |
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Authors: | Saralees Nadarajah Samuel Kotz |
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Institution: | (1) School of Mathematics, University of Manchester, Manchester, M60 1QD, UK;(2) Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC 20052, USA |
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Abstract: | Beta distributions are popular models for economic data. In this paper, six new distributions are introduced which generalize the standard beta distribution. These distributions involve the trigonometric functions, sine and cosine. Expressions are derived for their analytical shapes, nth moments, method of moments estimators, maximum likelihood estimators and the associated Fisher information matrices. These calculations involve several special functions. A numerical study is performed to show the flexility of these distributions as compared to the standard beta distribution. An application to consumer expenditure data is illustrated to show that the proposed distributions are better models to economic data than one based on the standard beta distribution. Possible ways of extending the models are also discussed. |
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Keywords: | Beta trigonometric distribution Cos distribution Sin distribution Fisher information matrices |
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