Sample Kurtosis Formula. Definition of kurtosis for univariate data y1 y2 yn the formula for kurtosis is. Thus with this formula a perfect normal distribution would have a kurtosis of three.
Note that in computing the kurtosis the standard deviation is computed using n in the denominator rather than n 1. Therefore sample kurtosis equals. Mean of samples x i the ith sample n.
Alternative definition of kurtosis.
I th variable of the distribution. Sample kurtosis is always measured relative to the kurtosis of a normal distribution which is 3. A normal curve has a value of 3 a leptokurtic has beta 2 greater than 3 and platykurtic has beta 2 less then 3. Therefore sample kurtosis equals.
