Confidence that data belongs to distribution

[coolnessitself]

Hi all,
This seems like a simple question, but I'm just not too knowledgeable about statistical methods.

I have a piecewise pdf $$f(x;\gamma)$$ (not any regular distribution) where $$\gamma$$ is known, and a set of non-uniformly spaced data points I obtained that somewhat resemble $$f(x;\gamma)$$. How do I go about finding some numeric value that shows the probability that my data comes from this distribution?
Also, once I'm able to do this, is there a methodology that allows me to find the best way the data fits, i.e. find $$x_\mathrm{shift}$$ such that if all data points are shifted right by $$x\rightarrow x+x_\mathrm{shift}$$, the data has the highest probability of coming from $$f(x;\gamma)$$?

(If it makes a difference, the pdf is http://nvl.nist.gov/pub/nistpubs/jres/106/2/j62mil.pdf" )

 

[bpet]

Would that be "maximum likelihood estimation", where the parameter to be estimated is xshift?