Kurtosis

Kurtosis is the measurement of tailedness of a distribution. The tailedness in distribution occurs when there are outliers present. Hence, excess kurtosis implies the tailedness of the distribution which is relative to the normal distribution (a symmetrical distribution with no skew).
 

Kurtosis reveals three types of distribution and they are:

• Medium kurtosis (medium tails) are mesokurtic
• Low kurtosis (thin tails) are platykurtic
• High kurtosis (fat tails) are leptokurtic

Mesokurtic:

A distribution that has tails shaped in roughly the same way as any normal distribution, but not the standard normal distribution, is said to be mesokurtic. The kurtosis of a mesokurtic distribution is neither high nor low.

Platykurtic:

Platykurtic distributions are those that have lean tails.  Many times they possess a peak lower than a mesokurtic distribution. All uniform distributions are platykurtic.

Leptokurtic:

A leptokurtic distribution has greater kurtosis than a mesokurtic distribution. Leptokurtic distributions are sometimes identified by peaks that are thin and tall. The tails of these distributions, to both the right and the left, are thick and heavy. One of the most well-known leptokurtic distributions is student's t distribution.

Tails represent the probability or frequency of values that are extremely high or low compared to the mean. In other words, tails represent how often outliers occur.