On Thu, 19 Oct 2000 17:53:41 +0900, "Choi, Young Sung"
<[EMAIL PROTECTED]> wrote:
> I am a statistically poor researcher and have a statistical problem.
>
> I have two candidate distributions, A(theta1) and B(theta1, theta2) to model
> my data.
> Then how should I determine the best distribution for my data?
> Suggest me an easy book that explain how to select a distribution when
> making a probability model and how to test the goodness of the selected
> distribution over other ones.
>
"Data Analysis, A Model Comparison Approach" by Judd and McClelland.
What you describe, assuming your notation is intentional, is a nesting
of one model within another. So the one with greater number of
parameters will have the better "fit" (at least, no worse) in an
absolute sense, and the question is whether the fit that is achieved
by using more parameters improves more than you should expect, for
that increase in parameters.
Assume that "fit" is measured by finding parameters satisfying
least-squares error, or by maximum-likelihood. (There are
other possibilities, but a similar logic generally applies.)
If we further assume independence and homogeneity, then the
improvement can be tested. Testing is often by an F-test that uses
the number of added-parameters as the number of "degrees of freedom"
in the numerator. Various texts will have this as the "Chow" test.
Finally, you SELECT a distribution according to what sense it makes,
and what purpose is served, and whether any good purpose is served by
using the more complex parameterization. In some fashion, you need to
justify the complexity or other costs of using more parameters. See
Robert Abelson, "Statistics as Principled Argument."
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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