As discussed: 
* when verifying whether samples are drawn from your distribution *p = dF*, you could transform your samples through the desired cdf *F*, which -- if samples are drawn from that distribution -- should result in a uniform distribution on the interval [0, 1]. You may then run any tests for uniformity.

* If you'd prefer to keep the current settings, then your test statistic is Cramér--Von Mises (up to a multiplication by the number of samples), or if you weigh your samples by F(1-F) -- weighing your tails more -- you'd get the Anderson--Darling statistic (again up to that multiplicative factor).

Hope this helps.