LOS L requires us to:
explain measures of sample skewness and kurtosis
a. Kurtosis is a statistical measure that tells us whether a distribution is more or less peaked than the normal distribution.
b. A distribution that is more peaked than normal is called leptokurtic; the one less peaked than normal a platykurtic; and the one symmetrical to the normal, a mesokurtic.
Thus, if the kurtosis is greater than 3 (or excess kurtosis is greater than zero), it is called leptokurtic; if it is equal to 3, it is called mesokurtic; and if it is less than 3, it is called platykurtic.
c. The formula for calculating the excess kurtosis of distribution is:
In the above equation, as ‘n’ gets larger, the value of ([n (n + 1)] / [(n – 1)(n – 2)(n-3)] ) gets closer to [1 / (n – 1)]; and [3 (n – 1)2] / [(n – 2)(n-3)] will get closer to 3. Thus, the value of excess kurtosis would be: