Biased distribution on semi-infinite axis

[mikeph]

Hi

Usually I'm used to dealing with symmetric distributions with mean at 0, but one has come up that cannot take this form because 0 is impossible to attain. Instead, this function seems to have a bell-shaped look, although the mean is around 5 and the tail towards 0 drops off a little bit faster than towards the positive infinity. Given that I know this distribution has a minimum above 0, are there any standard models that I can use for curve-fitting?

The Maxwell distribution looks similar, I think this is (x^2)*exp(-x^2) plus normalizing factors, but this still goes to zero- I suppose I can shift x but it's not very "tidy". I'm going to test it nevertheless, but I'd like to know if there are any other models I can compare it to for perspective?

Thanks

 

[mikeph]

Any ideas? It's got an incredibly small tail going leftwards...100,000 samples found a minimum of about 4.7, but I know it goes down below 3 at least.

Here's the shape

Maxwell's version won't work because I think the best fit will find a zero at about 4.5. I'm trying x^3 and x^4 versions but I'm not sure if they're going to work either.