Hi Bill..Thanks for your reply. You mentioned in the last line of your message that statistical tests are not a very good way to choose among distributions. If this is the case, what test do you think is better in my case??
Thanks... CCC "Bill Rowe" <[EMAIL PROTECTED]> wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... > 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 ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =================================================================
