The kurtosis of the geometric distribution is . The excess kurtosis of a distribution is the difference between its kurtosis and the kurtosis of a normal distribution, . Therefore, the excess kurtosis of the geometric distribution is . Since , the excess kurtosis is always positive so the distribution is leptokurtic. In other words, the tail of a geometric distribution decays faster than a Gaussian.
The kurtosis of the geometric distribution is  The excess kurtosis of a distribution is the difference between its kurtosis and the kurtosis of a normal distribution  Therefore the excess kurtosis of the geometric distribution is  Since  the excess kurtosis is always positive so the distribution is leptokurtic In other words the tail of a geometric distribution decays faster than a Gaussian