Structural properties of generalised Planck distributions

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