I don't recall seeing the Pearson-Fisher names associated in this way; however, beta2=mu4/(mu2)^2 is one of the two parameters defining the Pearson curves and this could account for its ascription to him. Fisher discussed cumulants quit a bit, and since k4/k2^2=beta2-3, this may account for that ascription.
Karl L. Wuensch wrote: > B2, the expected value of the distribution of Z scores which have > been raised to the 4th power, which has a value of 3 for a normal > distribution, is often referred to as "Pearson kurtosis." Subtract 3 > from this quantity and you get a parameter which is often referred to as > "Fisher kurtosis." For example, at > http://www2.chass.ncsu.edu/garson/pa765/assumpt.htm, you can find the > following: > > Kurtosis is the peakedness of a distribution. A common rule-of-thumb > test for normality is to run descriptive statistics to get skewness and > kurtosis, then divide these by the standard errors. Kurtosis also should > be within the +2 to -2 range when the data are normally distributed (a > few authors use +3 to -3). Negative kurtosis indicates too many cases in > the tails of the distribution. Positive kurtosis indicates too few cases > in the tails. Note that the origin in computing kurtosis is 3 and a few > statistical packages center on 3, but the foregoing discussion assumes > that 3 has been subtracted to center on 0, as is done in SPSS and > LISREL. The version with the normal distribution centered at 0 is Fisher > kurtosis, while the version centered at 3 is Pearson kurtosis. SPSS uses > Fisher kurtosis. Various transformations > <http://www2.chass.ncsu.edu/garson/pa765/assumpt.htm#transforms> are > used to correct kurtosis: cube roots and sine transforms may correct > negative kurtosis. > > Now I happen to think that this statement is dead wrong in > associating negative kurtosis with "too many cases in the tails" and > positive kurtosis with "too few cases in the tails," but I am not > looking to start an extended discussion of what the "tails" of a > distribution really are. > > My query to this group is: Why is B2 called Person kurtosis and (B2 > - 3) called Fisher kurtosis? Recently I read Pearson, K. (1905). Das > Fehlergesetz und seine Verallgemeinerungen durch Fechner und Pearson. A > Rejoinder. Biometrika, 4, 169-212, and in that interesting article > Pearson defined kurtosis as (B2 - 3). > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > Karl L. Wuensch, Department of Psychology, > East Carolina University, Greenville NC 27858-4353 > Voice: 252-328-4102 Fax: 252-328-6283 > [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]> > http://core.ecu.edu/psyc/wuenschk/klw.htm > -- Bob Wheeler --- http://www.bobwheeler.com/ ECHIP, Inc. --- Randomness comes in bunches. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
