Confidence that data belongs to distribution

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