is.PD {PEkit}

Test for the shape of the distribution

Description

This function performs a statistical test on the null hypothesis that a given sample's underlying distribution is the Poisson-Dirichlet distribution. It calculates a test statistic that is then used to gain a p-value from an empirical distribution of the statistic from simulated samples from a PD distribution.

Usage

is.PD(x, rounds)

Arguments

x

A discrete data vector.

rounds

How many samples are simulated to obtain the empirical distribution.

Details

The calculated test statistic is

W=\sum_{i=1}^n n_i^2 / n ,

which is calculated from the sample. Here n_i are the frequencies of each unique value in the sample. The MLE of \psi is then estimated from the sample with the function MLEp(), and an amount of samples equal to the input parameter rounds are generated with that estimate of \psi and sample size n. The test statistic W is then calculated for each of the simulated samples. The original W is then given a p-value based on what percentage of the simulated W it exceeds.

Value

A p-value.

References

Watterson, G.A., (1978), The homozygosity test of neutrality. Genetics. 88(2):405-417.

Examples

##Test whether a typical sample follows PD:
x<-rPD(100,10)
is.PD(x, 100)

##Test whether a very atypical sample where frequencies of different values
## are similar:

x<-c(rep(1, 200), rep(2, 200), rep(3, 200), rep(4, 200), rep(5,200))
is.PD(x,50)