Kurtosis Of Standard Normal Distribution. Let y be a random variable. It is common to compare the kurtosis of a distribution to this value.
This distribution has a kurtosis statistic. The kurtosis of any univariate normal distribution is 3. Mbox kurtosis frac sum i 1 n y i bar y 4 n s 4 3 this definition is used so that the standard normal distribution has a kurtosis of zero.
Now excess kurtosis will vary from 2 to infinity.
μ y and σ y denote y s mean and standard deviation respectively. Then the kurtosis of the distribution of y is e y μ y 4 σ y 4. Compared to a normal distribution its central peak is lower and broader and its tails are shorter and thinner. The first category of kurtosis is a mesokurtic distribution.
