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Confidence that data belongs to distribution

  1. Nov 6, 2009 #1
    Hi all,
    This seems like a simple question, but I'm just not too knowledgeable about statistical methods.

    I have a piecewise pdf [tex]f(x;\gamma)[/tex] (not any regular distribution) where [tex]\gamma[/tex] is known, and a set of non-uniformly spaced data points I obtained that somewhat resemble [tex]f(x;\gamma)[/tex]. 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 [tex]x_\mathrm{shift}[/tex] such that if all data points are shifted right by [tex]x\rightarrow x+x_\mathrm{shift}[/tex], the data has the highest probability of coming from [tex]f(x;\gamma)[/tex]?

    (If it makes a difference, the pdf is http://nvl.nist.gov/pub/nistpubs/jres/106/2/j62mil.pdf" [Broken])
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 8, 2009 #2
    Would that be "maximum likelihood estimation", where the parameter to be estimated is xshift?
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