A compound beta distribution with applications in finance |
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Authors: | Saralees Nadarajah Arjun K. Gupta |
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Affiliation: | (1) School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK;(2) Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA |
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Abstract: | If X and Y are gamma distributed independent random variables then it is well known that the ratio X / (X + Y) has the beta distribution. In this note, the distribution of W = X / (X + Y) is considered when X and Y have the compound gamma distribution. We refer to the distribution of W as compound beta and describe an application to consumer price indices to show that compound beta is a better model than one based on the standard beta distribution. We derive various properties of W, including its probability density function, cumulative distribution function, hazard rate function and moments. |
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