# Kurtosis

An expression of the so-called "fourth moment". A tendency for a distribution to form a sharp narrow peak in the center (or, when negative, a broad flat plateau). It is a unitless parameter. If the value is positive it indicates that the distribution of the signal has longer tails than the Gaussian distribution (a spikier signal). If the value is negative it indicates that the tails of the distribution are shorter than that of the Gaussian (a smoother function). The kurtosis is defined as

The -3 is necessary to make a Gaussian distribution have a kurtosis of zero.

Mesokurtic - normal distribution
Platykurtic - less peaked distribution
Leptokurtic - more peaked distribution

Standardized Kurtosis
A standardized form of the kurtosis statistic which renders the statistic free of scale. Standardized kurtosis can be used to test whether your data comes from a normal distribution. If it does, the statistic will fall between -2 and +2 about 95% of the time.

Subjects: Noise & Vibration