A generalized planck distribution |
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Authors: | Saralees Nadarajah Samuel Kotz |
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Affiliation: | (1) School of Mathematics, University of Manchester, M60 1QD Manchester, UK;(2) Department of Engineering Management and Systems Engineering, George Washington University, USA |
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Abstract: | We introduce a generalization of the standard Planck distribution discussed by Johnson and Kotz (1970, Section 33.6.1). This
generalization results in a very flexible family which contains the gamma distribution as a particular case. In this paper
we provide a comprehensive treatment of the mathematical properties of the family. We derive expressions for thenth moment, moment generating function, characteristic function, mean deviation about the mean, mean deviation about the median,
Rényi entropy, Shannon entropy and the asymptotic distribution of the extreme order statistics. Estimation and simulation
issues are also considered. |
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Keywords: | Gamma distribution generalized Planck distribution Planck distribution |
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