Re: Goodness of fitting of a distribution


Herman Rubin wrote:
In article <1162867197.824670.102540@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Reef Fish <large_nassua_grouper@xxxxxxxxx> wrote:

Beliavsky wrote:
nelson wrote:
hi all!
i have done some fitting test of a dataset. I do quantile quantile
plot that points out that the best distribution that fit my data is a
linear combination of a weibull and a normal distribution. How can i
have a teorical test that can confirm it? People that work with me
wants to see numbers, not only QQ plots. And they don't like sum of
square error...

You can use the Kolmogorov-Smirnov test of goodness-of-fit

Kolmogorov-Smirnov statistics is NOT a "goodness of fit" statistic.

It is the maximum order statistic between a theoretical cdf and
an empirical cdf. It is a statistic sometimes used to measure
the DEPARTURE from a given cdf, rather than a "goodness of
fit".

I do not know of any "goodness of fit" test which is
not a "badness of fit" test.

Then perhaps you don't know as many tests as you think, and
you also over-value the K-S stat which examines ONE value
(the max) in the difference between two cdfs.

It is a TERRIBLE measure of "goodness of fit" because it looks
at only the point of MAXIMUM discrepancy.

Terrible? Very definitely NOT. In a given situation,
there may well be better tests, but it has comparable
power to parametric tests, and it is a universal test.

It is the chi-squared test with many classes which has
little power, and the combination of local discrepancies
with the same direction adds greatly to the power. The
maximum takes advantage of this.

You found one that is WORSE than the K-S test. :-)

And even THAT is not strictly worse except against LONG-
tailed distirubtions, where a Chi-square goodness of fit
test necessarily lumps the information in the TAILS that is
most telling into the end bins.

For short-tail distribution, such as the Uniform, the Chi-
square goodness if fit ain't too bad. In fact, is is used as
ONE of the tests for pseudorandom number generators.
To test the uniformity of the distribution in ALL bins.

-- Reef Fish Bob.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558

.

Relevant Pages

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  • Re: Goodness of fitting of a distribution
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    (sci.stat.math)
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