Zero Inflated Poisson Distribution: Fail to estimate the parameter with error code 100

Question

Following is a kind of data set I am working on it:

data <- c(0, 1, 0, 11, 2, 0, 3, 0, 0, 2, 1, 3, 1, 0, 1, 0, 0, 0, 2, 3, 
0, 0, 0, 8, 1, 1, 1, 0, 1, 1, 2, 7, 0, 0, 0, 5, 2, 3, 6, 1, 1, 
5, 2, 9, 0, 0, 1, 21, 16, 2, 9, 6, 25, 2, 1, 12, 16, 14, 15, 
15, 6, 1, 12, 12, 13, 5, 5, 6, 4, 7, 11, 8, 4, 5, 8, 3, 8, 4, 
7, 4, 7, 2, 5, 6, 4, 5, 1, 0, 8, 5, 6, 8, 9, 8, 9, 7, 7, 9, 8, 
9, 4, 4, 7, 13, 9, 13, 12, 10, 9, 8, 7, 11, 5, 5, 0, 1, 33, 4, 
22, 19, 22, 9, 5, 4, 17, 7, 7, 4, 5, 3, 0, 0, 9, 3, 0, 0, 36, 
40, 5, 4, 0, 11, 0, 7, 5, 25, 39, 26, 4, 20, 12, 4, 17, 3, 22, 
12, 14, 8, 9, 11, 7, 11, 10, 9, 16, 6, 24, 8, 5, 6, 14, 3, 9, 
4, 1, 20, 0, 1, 7, 9, 0, 12, 2, 29, 56, 16, 8, 28, 0, 19, 25, 
35, 87, 56, 66, 60, 58, 14, 10, 12, 13, 13, 34, 26, 18, 13, 22, 
13, 12, 15, 41, 11, 11, 11, 5, 6, 7, 8, 8, 17, 16, 12, 21, 38, 
34, 10, 77, 41, 7, 12, 1, 16, 20, 8, 5, 2, 20, 7, 16, 12, 6, 
10, 31, 12)

I have used the fitdistrplus package to fit distribution using maximum likelihood.
Similarly, gamlss package defines the pdf, CDF of zero Inflated Poisson distribution.

library(fitdistrplus)   
library(gamlss)  

Here is the mean and standard deviation of the data set.

mu=mean(data)
sigma=sd(data)

The mean of the data set is 10.75 and the standard deviation is 13.050. I have tried to fit the zero-inflated Poisson distribution using fitdist function as below.

fit_zip = fitdist(data, 'ZIP', start = list(mu = mu, sigma = sigma))

Once the stated function is compiled then the compiler throws the following error

Error in fitdist(data, "ZIP", start = list(mu = mu, sigma = sigma)) : 
  the function mle failed to estimate the parameters, 
                with the error code 100

It is obvious that there is a problem in the initialization of the starting value of mu and sigma. I am not sure on what basis starting values are initialized.
any help is appreciated.

Answer 1

You could use VGAM::*zipois() instead of gamlss.dist::*ZIP() . The starting parameters are a bit different, see ?dzipois , and don't necessarily have to be the mean of your input.

library('fitdistrplus')
library('VGAM')  
fitdist(x, 'zipois', start=list(lambda=1, pstr0=.1))
# $start.arg
# $start.arg$lambda
# [1] 1
# 
# $start.arg$pstr0
# [1] 0.1
# 
# 
# $fix.arg
# NULL
# 
# Fitting of the distribution ' zipois ' by maximum likelihood 
# Parameters:
#   estimate Std. Error
# lambda 12.2009631 0.23823650
# pstr0   0.1187056 0.02069464
# Warning messages:
#   1: In fitdist(x, "zipois", start = list(lambda = 1, pstr0 = 0.1)) :
#   The dzipois function should return a zero-length vector when input has length zero
# 2: In fitdist(x, "zipois", start = list(lambda = 1, pstr0 = 0.1)) :
#   The pzipois function should return a zero-length vector when input has length zero

I'm not sure about the warning, though.

You may compare this by using a different vector x1 (below) which won't fail with gamlss.dist .

---

Data:

x <- c(0, 1, 0, 11, 2, 0, 3, 0, 0, 2, 1, 3, 1, 0, 1, 0, 0, 0, 2, 3, 
0, 0, 0, 8, 1, 1, 1, 0, 1, 1, 2, 7, 0, 0, 0, 5, 2, 3, 6, 1, 1, 
5, 2, 9, 0, 0, 1, 21, 16, 2, 9, 6, 25, 2, 1, 12, 16, 14, 15, 
15, 6, 1, 12, 12, 13, 5, 5, 6, 4, 7, 11, 8, 4, 5, 8, 3, 8, 4, 
7, 4, 7, 2, 5, 6, 4, 5, 1, 0, 8, 5, 6, 8, 9, 8, 9, 7, 7, 9, 8, 
9, 4, 4, 7, 13, 9, 13, 12, 10, 9, 8, 7, 11, 5, 5, 0, 1, 33, 4, 
22, 19, 22, 9, 5, 4, 17, 7, 7, 4, 5, 3, 0, 0, 9, 3, 0, 0, 36, 
40, 5, 4, 0, 11, 0, 7, 5, 25, 39, 26, 4, 20, 12, 4, 17, 3, 22, 
12, 14, 8, 9, 11, 7, 11, 10, 9, 16, 6, 24, 8, 5, 6, 14, 3, 9, 
4, 1, 20, 0, 1, 7, 9, 0, 12, 2, 29, 56, 16, 8, 28, 0, 19, 25, 
35, 87, 56, 66, 60, 58, 14, 10, 12, 13, 13, 34, 26, 18, 13, 22, 
13, 12, 15, 41, 11, 11, 11, 5, 6, 7, 8, 8, 17, 16, 12, 21, 38, 
34, 10, 77, 41, 7, 12, 1, 16, 20, 8, 5, 2, 20, 7, 16, 12, 6, 
10, 31, 12)

x1 <- 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)