The KS an related tests are not appropriate in this case because their sampling distributions depend on the estimators used to estimate the parameters of the various distributions. Another approach is to use a model selection criterion such as those of Akaike or Schwartz. Essentially these use a penalized likelihood value, with the penalties being functions of the number of parameters estimated. They are widely used in econometrics and any graduate level text on econometrics would describe them.
Paul Bill Rowe wrote: > > 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. > > -- > - > PGPKey fingerprint: 6DA1 E71F EDFC 7601 0201 9243 E02A C9FD EF09 EAE5 -- Paul L. Fackler Department of Agricultural and Resource Economics North Carolina State University Raleigh, NC 27695-8109 919-515-4535 [EMAIL PROTECTED] www4.ncsu.edu/~pfackler ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =================================================================
