In article <a0v9sk$j7j$[EMAIL PROTECTED]>,
"Chia C Chong" <[EMAIL PROTECTED]> wrote:
>I have a set of data with some kind of distribution. When I plotted the
>histogram density of this set of data, it looks sth like the
>Weibull/Exp/Gamma distribution. I find the parameters that best fit the data
>and then, plot the respective distribution using the estimated parameters on
>the empirical distribution. My question is, what kind of statistical test
>that I should use so that I will know which estimated distribution will fit
>the data better?? I need some kind of test that will give me some numerical
>values which distribution is fit better rather than just observed the
>fitting graphically..
Probably computing the Kolmogorov-Smirnov statistic or one of its
variants would suit your need.
Let Fn(x) = (number of X1, X2 ... Xn <= x)/n
Let F(x) be the cumalative distribution function of interest
Then the KS statistic is max(abs(Fn(x) - F(x)), i.e., the maximum
deviation of the observed cumualtive distribution function to the
expected cumulative distribution function.
the probability KS/sqrt(n) <= x approaches 1 - exp(-x^2) as x approaches
infinity.
Now having said this, the better way to choose among distributions would
be to base the choice on characteristics of the thing being measured.
For example, suppose I was measuring the time to the next drop of rain
in a fixed area during a rainstorm with a constant average rainfall.
That distribution should be exponential. It might be for any data set
collected either a gamma or a weibull distribution might fit the data
better, but it would still be more correct to assume an exponential for
this example.
In short, statistical tests are not a very good way to choose among
distributions.
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