Author: Dann Corbit
Date: 13:33:19 06/04/02
Go up one level in this thread
On June 04, 2002 at 16:18:10, Roy Eassa wrote: >On June 04, 2002 at 16:08:25, Dann Corbit wrote: > >>On June 04, 2002 at 16:06:55, Roy Eassa wrote: >> >>>On June 04, 2002 at 14:58:49, Dann Corbit wrote: >>> >>>>On June 04, 2002 at 14:13:43, Rolf Tueschen wrote: >>>> >>>>>I just saw your article. Could you add your opinion about how SSDF actually has >>>>>shown that computer strength is on a normal distribution? For weeks now or >>>>>better years I say it is not. It's a pity, but without that explanation you >>>>>invested so much precious time for nothing! I will answer in detail after your >>>>>explanation. >>>> >>>>SELECT int(rating/100), count([Rating]/100) >>>>FROM SSDF >>>>GROUP BY int([Rating]/100); >>>> >>>>Expr1000 Expr1001 >>>>14 2 >>>>15 12 >>>>16 12 >>>>17 23 >>>>18 21 >>>>19 22 >>>>20 17 >>>>21 25 >>>>22 23 >>>>23 18 >>>>24 20 >>>>25 18 >>>>26 15 >>>>27 5 >>>> >>>>Happy explaining. >>> >>> >>>Just an observation: that's no bell curve. >> >>It's a pedagogic example of a platykurtotic bell curve. > > >OK, that sent me scurrying to a search engine. > >"Kurtosis: >A measure of the extent to which observed data fall near the center of a >distribution or in the tails. A kurtosis value less than that of a standard, >normal distribution indicates a distribution with a fat midrange on either side >of the mean and a low peak-a platykurtotic distribution. A kurtosis value >greater than that of a normal distribution indicates a high peak, a thin >midrange, and fat tails. The latter, a leptokurtotic distribution, is common in >observed price, rate, and return time series data." > > >Does this mean it still IS a normal distribution? (It has 2 fairly large peaks >and one smaller one, from what I can tell.) Partly it is an artifact of the binning chosen, and partly more than one curve superimposed on the other (after all, they do change the speed of the machines from time to time). It may have some binomial component. An example of something that models that is heights of humans. You have one hump for men and one for women in the curve, so it has a dip in it. Here are some frequently used distributions: Beta Binomial Cauchy Chi square Erlang Extreme value (type 1, 2, generalized; and hence Gumbel, Fréchet) Gamma (standard & generalized) Hypergeometric Inverse of standard normal Inverse-normal CDF Logarithmic series (discrete) Logistic (standard & generalized) Negative binomial Negative exponential Non-central T Pareto (standard & generalized) Rayleigh Rice Snedecor-F Standard normal Student-T Tukey-lambda Von Mises Wakeby Weibull Here are some pictures: http://la.znet.com/~sdsampe/distr.htm#1 >I also found this: > >"The standard normal density has the familiar shape of the Bell Curve." > >Which is what I had been thinking when I posted the comment about this not being >a bell curve. It isn't a perfectly formed bell curve, but it is well enough formed for the statistical inferences to remain valid. Things like Erlang or exponential won't model as well with the standard ELO type calculations. The question we should ask is: Does the win expectancy predicted match that which is seen and how well? The answer is seen in the error bars. In fact, the model fit is excellent. An interesting paradox of statistics when doing fits (consider Chi-Squared) is that if the curve fits too well, it calls the experiment into question!
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