Donald Burrill wrote: > > I believe that at one time it may have been believed (or perhaps more > correctly, hoped) that knowledge of the first four central moments > would provide a useful empirical way of describing the shape of an > empirical distribution, much as a polynomial of degree 4 can > sometimes provide not too bad a description of many empirical > functions (over a limited range > of values, of course). But in practice this seems never to have > happened: perhaps because in practice one is concerned largely with > the shape of the tails of distributions, not with the shape of their > central 75% (say).
I think that recent workers would disagree with this in a subtle way. There has been some work an alternatives to moments as descriptors, notably L-moments. Papers on L-moments suggest that a major reason for not using ordinary moments is related to sampling variability: you need an extremely large sample to get a reasonable estimate of skewness and kurtosis. Again, there are problems with the skewness (and kurtosois) cofficient, in that, for a given sample size, the range of possible sample values is bounded. A slightly different point is that the "method of moments" is quite often used in fitting parametric distributions, although often with poor results. David Jones . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
