# Distribution of count data with large spread and heavy concentration of small values

I have a dataset of the counts of each user visiting a set of websites in a year (each user visits at least 1 website in my data). Half of the users visit 7 or fewer sites though the top user visits 9384 sites. I want to find a count distribution that can fit the data well but it seems challenging.

Here is the data summary:

• 46285 observations
• Mean: 33.1
• Std. Dev.: 138.5
• Skewness: 20.0 Kurtosis: 808.1

Percentile: Value - Smallest

• 1%: 1 - 1
• 5%: 1 - 1
• 10%: 1 - 1
• 25%: 1 - 3

Median

• 50%: 7

Percentile: Value - Largest

• 75%: 19 - 4947
• 90%: 53 - 5281
• 95%: 116 - 7111
• 99%: 522 - 9384

I tried Poisson which obviously doesn't work because mean << std. dev. Negative binomial does not do too much better.

Any suggestions?

Thanks!

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For things like this, the received wisdom seems to be a power law: en.wikipedia.org/wiki/Power_law How does that fit? – Ross Millikan Jul 28 '12 at 3:33
That's not a count model though isn't it. The values here have to be count values. – user18115 Jul 28 '12 at 4:01
you make your data continuous, so the probability of a given number goes as $n^{-k}$ for some $k$ chosen to fit the data. – Ross Millikan Jul 28 '12 at 14:22
That's not even a distribution isn't it. I can't ask what the probability that the number of visits is $k$ is. For what it's worth, I tried exponential distribution en.wikipedia.org/wiki/Exponential_distribution and it's also a bad fit. Again it's not discrete distribution. – user18115 Jul 28 '12 at 18:19