what is suitable probability distribution for count data

Question

My data set is about user creating files during one year. Frequencies are

number of files / freq
 0   49
 1   36
 2   42
 3   26
 4   22
 5   22
 6    8
 7   12
 8    2
 9    4
10    7
11    0
12    1
13    1
14    1
15    1
16    2
17    1
18    0
19    1
20    0

What is most suitable distribution for this data set. I excluded vecation days since, and Saturday and Sunday. Distribution is needed to model this user in simulation. My row data clearly you can see that vacation is from 15.07 until 18.08 that s why there is empty part on chart.

Answer 1

Two common distributions for count data are the poisson or the negative-binomial one. If we fit these to your data, the NB works a lot better:

library(MASS) # for fitdistr()

xx <- 0:20
counts <- c(49, 36, 42, 26, 22, 22, 8, 12, 2, 4, 7, 0, 1, 1, 1, 1, 2, 1, 0, 1, 0)
obs <- rep(xx,counts)

poisson.density <- length(obs)*dpois(xx,mean(obs))
nb <- fitdistr(obs,"negative binomial")
nb.density <- length(obs)*dnbinom(xx,size=nb$estimate["size"],mu=nb$estimate["mu"])

foo <- barplot(counts,names.arg=xx,ylim=range(c(counts,poisson.density)))
lines(foo[,1],poisson.density,lwd=2)
lines(foo[,1],nb.density,lwd=2,col="red")
legend("topright",lwd=2,col=c("black","red"),legend=c("Poisson","Negative Binomial"))

However, there seems to be a peak at zero. Might there be a separate process that leads to zeros? If so, you might want to look at zero-inflation, e.g., the zero-inflated Poisson (ZIP).

You say that you have already removed weekends. You might still have intra-weekly seasonality (e.g., on Fridays), so you might want to consider modeling these in a regression framework, e.g., using Poisson regression or negative binomial regression. Then again, this might be overkill.

Finally, if all you are interested in is simulation, you could simply resample from the data you already have. Or fit a semiparametric kernel density to your observed frequencies and sample from that.