Tests for goodness-of-fit based on the empirical distribution function are pretty standard fare. Their applicability relies on the Glivenko-Cantelli Theorem.
However, things get a little tricky when the data are discrete (rather than continuous), or when they are "circular" in nature. When the data exhibit both of these characteristics, some really interesting testing issues have to be handled.
A paper that I wrote a short while back on this topic has just been accepted for publication in the Chilean Journal of Statistics. The paper is titled, "Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications", and it'll be appearing in the 2013 volume of the journal.
However, things get a little tricky when the data are discrete (rather than continuous), or when they are "circular" in nature. When the data exhibit both of these characteristics, some really interesting testing issues have to be handled.
A paper that I wrote a short while back on this topic has just been accepted for publication in the Chilean Journal of Statistics. The paper is titled, "Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications", and it'll be appearing in the 2013 volume of the journal.
You can download a copy of the paper here.
© 2012, David E. Giles
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