Hi,
This is a problem I have been wrestling with for sometime, and would
appreciate any thoughts, references or comments.
I have a routine which I claim produces a sequence of random numbers from a
given distribution, say a normal distribution. How do I test this claim?
The "random" part of the question is fairly well covered in the literature,
but the testing that the sequence comes from a normal distribution isn't.
As far as I can tell most of the tests, for example Chi-squared, Kruskal
Wallis, Anderson-Darling etc are of the form:
H0: Sequence is from a normal distribution vs H1: Sequence is not from a
normal distribution
Therefore only give definitive information if the null hypothesis is
rejected (i.e. there is evidence that the sequence is not from a normal
distribution). A similar problem occurs when comparing the observed and
theoretical moments using CIs.
The best I have so far come up with is to compare the absolute difference
between the observed and theoretical moments to some fixed (and arbitrary)
tolerance (as this requires a fairly large sample size to be used), and
perform a chi-squared test as well. This doesn't, however, seem
satisfactory.
This process needs to be repeated for a number of different routines /
distributions.
Thanks in advance for your help,
Martyn
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