# An alternative to a regular poisson distribution for count data.

I'm trying to find out what distribution my empirical count data fits. Scores can run from 0-8 and I have ~360 observations. I've been using the fitdistrplus package and have tested a poisson distribution. The gof stats I got were:

Fitting of the distribution ' pois ' by maximum likelihood
Parameters :
estimate Std. Error
lambda 4.490489 0.07811023
Loglikelihood:  -1571.578   AIC:  3145.155   BIC:  3149.756


I tried testing a negative binomial also but got this error message:

> fitnbinom <-fitdist(survival,"nbinom")
Warning messages:
1: In dnbinom(c(4L, 3L, 1L, 1L, 6L, 5L, 4L, 3L, 4L, 1L, 0L, 0L, 6L,  :
NaNs produced
2: In dnbinom(c(4L, 3L, 1L, 1L, 6L, 5L, 4L, 3L, 4L, 1L, 0L, 0L, 6L,  :
NaNs produced


I'm not sure the fit of the Poisson is that good so would like to test an alternative. Any suggestions? Also any help with the code for testing an alternative in fitdistrplus would be great - The examples provided in the vignette for count data test a Poisson and negative binomial but no others. I'm aware that you can test distributions provided in other packages but I haven't been able to work out how to do this.

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• If it's bounded between 0 and 8, I wouldn't start with a Poisson. But why do you need to fit a distribution at all? – Glen_b Sep 9 '15 at 10:12
• I need to test a mixed effects model and would like to know what distribution best fits the data so I can (attempt to) specify this in the model. – keelybebbington Sep 10 '15 at 10:48
• I don't see how the unconditional distribution of the response tells you what that should be. – Glen_b Sep 10 '15 at 10:59
• I'm not sure what you mean. What would you suggest I do to check what distribution fits the data best? – keelybebbington Sep 11 '15 at 6:09