### Is this a known probability distribution?

Posted:

**Thu Aug 10, 2017 5:38 am UTC**Originally posted on stackexchange, but with no answers or even comments, I'm posting it here:

For work, I plotted a set of shops by how many times they did business in the past week. The plot I got out looked something like this:

This looked obviously like a Pareto distribution. After all, that's the distribution of earthquakes and rich people. It would make sense in this sort of context. However, when plotting the log-log of this graph, instead of a straight line, I get this:

After further play with the data, I found that this curve could be straightened if I took a root of the log of the y value (in this case, the 3.9th root), and from that I derived a general formula for this and similar distributions I had seen:

p=exp(

where k,a,b are all positive

I've done various searches and have looked through lists of named distributions, and haven't come across any distributions that resemble this one. Is this a known distribution?

For work, I plotted a set of shops by how many times they did business in the past week. The plot I got out looked something like this:

This looked obviously like a Pareto distribution. After all, that's the distribution of earthquakes and rich people. It would make sense in this sort of context. However, when plotting the log-log of this graph, instead of a straight line, I get this:

After further play with the data, I found that this curve could be straightened if I took a root of the log of the y value (in this case, the 3.9th root), and from that I derived a general formula for this and similar distributions I had seen:

p=exp(

^{k}√(-a log(x)+b))where k,a,b are all positive

I've done various searches and have looked through lists of named distributions, and haven't come across any distributions that resemble this one. Is this a known distribution?