Structural properties of generalised Planck distributions

Anthony G. Pakes ()
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Anthony G. Pakes: Univ. of Western Australia

Journal of Statistical Distributions and Applications, 2021, vol. 8, issue 1, 1-33

Abstract: Abstract A family of generalised Planck (GP) laws is defined and its structural properties explored. Sometimes subject to parameter restrictions, a GP law is a randomly scaled gamma law; it arises as the equilibrium law of a perturbed version of the Feller mean reverting diffusion; the density functions can be decreasing, unimodal or bimodal; it is infinitely divisible. It is argued that the GP law is not a generalised gamma convolution. Characterisations are obtained in terms of invariance under random contraction of a weighted version of a related law. The GP law is a particular instance of equilibrium laws obtained from a recursion suggested by a genetic mutation-selection balance model. Some related infinitely divisible laws are exhibited.

Keywords: Planck distribution; Mean reverting diffusion; Modal properties; Infinite divisibility and self-decomposability; Length biased and weighted laws; Characterisation; Mutation-selection balance; 60E05; 62E10; 60E07; 60J60; 92D10 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00124-1

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DOI: 10.1186/s40488-021-00124-1

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