Fitting a zero inflated poisson distribution in R
I have a vector of count data that is strongly over dispersed and zero inflated.
The vector looks like this:
i.vec=c(0,63,1,4,1,44,2,2,1,0,1,0,0,0,0,1,0,0,3,0,0,2,0,0,0,0,0,2,0,0,0,0,
0,0,0,0,0,0,0,0,6,1,11,1,1,0,0,0,2)
m=mean(i.vec)
# 3.040816
sig=sd(i.vec)
# 10.86078
I would like to fit a distribution to this, which I strongly suspect will be a zero inflated poisson (ZIP). But I need to perform a significance test to demonstrate that a ZIP distribution fits the data.
If I had a normal distribution, I could do a chi square goodness of fit test using the function goodfit() in the package vcd, but I don't know of any tests that I can perform for zero inflated data.
Answer
Here is one approach
# LOAD LIBRARIES
library(fitdistrplus) # fits distributions using maximum likelihood
library(gamlss) # defines pdf, cdf of ZIP
# FIT DISTRIBUTION (mu = mean of poisson, sigma = P(X = 0)
fit_zip = fitdist(i.vec, 'ZIP', start = list(mu = 2, sigma = 0.5))
# VISUALIZE TEST AND COMPUTE GOODNESS OF FIT
plot(fit_zip)
gofstat(fit_zip, print.test = T)
Based on this, it does not look like ZIP is a good fit.