With the Shifted Exponential test, H_0 is "data is a sample coming from a Shifted Exponential distribution with shift=30 and lambda = 0.001566907"
You appear to be applying the KS test after estimating parameters.
I do in order to define H_0 as explained above
The distribution theory is for an iid sample from a known continuous distribution (and does not otherwise depend on the distribution).
That's what I thougth but this is not what I understand reading: http://www.isi.edu/~kclan/paper/ramp/node11.html
Since your H_0 is not pre-specified, that distribution theory is not correct.
please see above
(Some corrections have been worked out for say ML fitting of exponential and normal distributions -- by Michael Stephens as I recall.) Also, your `truncated LogNormal' does not appear to be truncated, rather to be shifted. That's the same thing for an exponential (for a positive shift), but not for any other distribution.
Thanks for this clarification
And what is the H_0 and H_1 used in the article?
H_1 is that the sample is not coming from the specified distribution in H_0
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