ickePoissonisk

ickePoissonisk is a term used in statistics and related fields to describe phenomena whose counting statistics depart from Poisson behavior. The word blends icke, an inflected form of "not" in several Scandinavian languages, with Poissonisk, meaning "Poissonian." In usage, ickePoissonisk designates processes whose inter-arrival times are not exponentially distributed and whose variance does not equal the mean, in contrast to a Poisson process.

In formal terms, let N(t) be a counting process with mean μ(t)=E[N(t)] and variance σ^2(t)=Var[N(t)]. If σ^2(t) = μ(t) for all t, the process is Poissonian; otherwise it is ickePoissonisk. The Fano factor F(t) = σ^2(t)/μ(t) differs from 1. Inter-arrival time distribution is not exponential; renewal properties may or may not hold. Sub-Poissonian (F<1) or super-Poissonian (F>1) are common subcategories of ickePoissonisk.

Contexts where the term appears include quantum optics, biology, ecology, and telecommunications. In quantum optics, sub-Poissonian light exhibits reduced variance in photon counts and antibunching, a hallmark of non-Poissonian statistics. In biology, bursting gene expression or irregular neuronal spike trains often show ickePoissonisk statistics. In telecommunications, bursty traffic can produce non-Poissonian arrival processes. The term is not universally standardized; some authors prefer "non-Poissonian" or "non-Poisson statistics."