# Can a negative binomial distribution be used to model a continuous distribution?

I have a data set which is a set of continuous distances from some origin. I originally modeled this as a negative binomial distribution by rounding the data and using it as an input in the Matlab function, nbinfit:

nbReg = nbinfit(round(data));


Using the output from nbinfit, I created the following CDF:

Here are the corresponding QQ Plots

Questions

1. Is it valid to use a negative binomial distribution to model a continuous distribution? Is there any documentation in the literature where negative binomial was used to model continuous data?

2. It is possible to have a similarly distributed continuous distribution
(you can remove the x == round(x) condition in nbinpdf to get a continuous distribution)?

3. The CDF fits very well, but is there a "better" distribution you would recommend?**

-
 Those don't look like good fits. Plotting a CDF against an EDF is not very revealing: use probability plots instead. – whuber♦ Jul 14 '11 at 15:33 @Whuber, added QQ plots to question – Elpezmuerto Jul 14 '11 at 15:37