
KURTOSISName:
Kurtosis is a measure of how heavy tailed a distribution is. A normal distribution has a kurtosis of 3. A kurtosis greater than 3 indicates that the data is heavy tailed (i.e., more spread out) relative to a normal distribution while a kurtosis value less than 3 indicates that the data is light tailed (i.e., more compressed) relative to a normal distribution. Some sources subtract 3 from the kurtosis value in order to make the kurtosis 0 for a normal distribution. We refer to this as the "excess kurtosis" statistic.
where <y> is the response variable; <par> is a parameter where the calculated kurtosis is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax returns the conventional kurtosis statistic (i.e., 3 is not subtracted).
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the calculated kurtosis is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax returns the excess kurtosis statistic (i.e., 3 is subtracted).
LET A1 = KURTOSIS Y1 SUBSET Y1 > 2 LET A1 = EXCESS KURTOSIS Y1
STANDARDIZED 4TH CENTRAL MOMENT
2014/12: Added EXCESS KURTOSIS statistic 2014/12: Changed from N1 to N in the formula LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 LET Y2 = DOUBLE EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 100 LET Y3 = SLASH RANDOM NUMBERS FOR I = 1 1 100 LET Y4 = CAUCHY RANDOM NUMBERS FOR I = 1 1 100 LET A1 = KURTOSIS Y1 LET A2 = KURTOSIS Y2 LET A3 = KURTOSIS Y3 LET A4 = KURTOSIS Y4 SET WRITE DECIMALS 3 PRINT A1 A2 A3 A4The following output is generated PARAMETERS AND CONSTANTS A1  4.217 A2  3.948 A3  29.870 A4  52.326  
Privacy
Policy/Security Notice
NIST is an agency of the U.S. Commerce Department.
Date created: 12/14/2014 