What are the differences between a platykurtic a mesokurtic and a leptokurtic distribution?

Answer 1

The kurtosis of a distribution is defined as the fourth central moment divided by the square of the second central moment. Unfortunately, this browser converts Greek characters to the Roman alphabet so I cannot use standard forms of equations but:

Suppose that for a random variable X, E(X) = m (mu)

and E[(X - E(X))2] = V = s2 (sigma-squared)

then

Kurtosis = E[(X - E(X))4]/s4.

Excess Kurtosis is then Kurtosis - 3.

If excess kurtosis < 0 the distribution is platykurtic. They have a peak that is lower than the Normal: the peak is flat and broad. The tails of the distribution are narrow. Uniform distributions are platykurtic.

A mesokurtic distibution has excess kurtosis = 0. The Gaussian (Normal) distribution - whatever its parameters - is mesokurtic. The binomial with probability of success close to 1/2 is also considered to be mesokurtic.

If excess kurtosis is > 0 the distribution is leptokurtic. Leptokurtic distributions have a high and narrow peak. A good example is the Student's t distribution.