arXiv subjects
Publications and source records attributed to Thierry E Huillet.
We describe recursive chance mechanisms and processes involving Zipf's law and relatives, all showing up mixing properties, both geometric and Poisson. Relations to Markov processes are explored.
We show that the Sibuya distribution and its non-critical relatives are relevant in the context of the recursive generation of both simply generated and increasing critical trees' and forests' progenies. A special class of generalized Stirling numbers are at the heart of the analysis of the induced occupancy distributions. Asymptotic aspects of large forests are addressed.
In a family of random variables, Taylor's law or Taylor's power law offluctuation scaling is a variance function that gives the variance $σ^{2}>0$ of a random variable (rv) $X$ with expectation $μ>0$ as a powerof $μ$: $σ^{2}=Aμ^{b}$ for finite real $A>0,\ b$ that are thesame for all rvs in the family. Equivalently, TL holds when $\log σ^{2}=a+b\log μ,\ a=\log A$, for all rvs in some set. Here we analyze thepossible values of the TL exponent $b$ in five families of infinitelydivisible two-parameter distributions and show how the values of $b$ dependon the parameters of these distributions. The five families areTweedie-Bar-Lev-Enis, negative binomial, compound Poisson-geometric,compound geometric-Poisson (or Pólya-Aeppli), and gamma distributions.These families arise frequently in empirical data and population models, and they are limit laws of Markov processes that we exhibit in each case.