dPD: The Poisson-Dirichlet distribution

In ville-kinnula/SPEC: Supervised Classification under Partition Exchangeability

Description

Distribution function for the Poisson-Dirichlet distribution.

Usage

dPD(abund, psi)

Arguments

abund	An abundance vector.
psi	Dispersal parameter. Accepted values are positive numbers, "a" for absolute value ψ=1 by default, or "r" for relative value psi equals sample size.

Details

dPD calculates the probability of a data vector x given by the Poisson-Dirichlet distribution, also known as the Ewens sampling formula. The higher the dispersal parameter ψ, the higher the amount of distinct observed species. In terms of the paintbox process, a high ψ increases the size of the continuous part p_0 of the process, while a low ψ will increase the size of the discrete parts p_>0.

Value

dPD returns the probability of the abundance vector of the data vector x, given dispersal parameter ψ.

References

W.J. Ewens, The sampling theory of selectively neutral alleles, Theoretical Population Biology, Volume 3, Issue 1, 1972, Pages 87-112, ISSN 0040-5809, https://doi.org/10.1016/0040-5809(72)90035-4.

Examples

## Get a random sample from the Poisson Dirichlet distribution, and
## find the probability of such a sample with psi=5:
set.seed(111)
s <- rPD(n=100,psi=5)
a=table(table(s))
dPD(a, psi=5)

ville-kinnula/SPEC documentation built on Dec. 23, 2021, 3:11 p.m.