MLEp {PEkit}

Maximum Likelihood Estimate of \psi

Description

Numerically searches for the MLE of \psi given an abundance vector with a binary search algorithm.

Usage

MLEp(abund)

Arguments

abund

An abundance vector.

Details

Numerically searches for the MLE of \psi as the root of equation

K=\sum_{i=1}^n\psi/(\psi+i-1),

where K is the observed number of different species in the sample. The right side of the equation is monotonically increasing when \psi>0, so a binary search is used to find the root. An accepted \psi sets value of the right side of the equation within R's smallest possible value of the actual value of K.

Value

The MLE of \psi.

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, <doi: 10.1016/0040-5809(72)90035-4>.

Examples

##Find the MLE of psi of the vector (1,2,2).
##The frequencies of the frequencies of the data vector are given as input:
MLEp(abundance(c(1,2,2)))

##Find the MLE of psi of a sample from the Poisson-Dirichlet distribution:
set.seed(1000)
x<-rPD(n=10000, psi=100)
MLEp(abundance(x))