kurtosis

It is defined as the kurtosis of the order parameter.

The kurtosis is here defined to be the standardised fourth moment around the mean.

In the images on the right, the blue curve represents the density with kurtosis of 2.

Notice that the degrees of freedom is sometimes known as the kurtosis parameter.

The kurtosis in both these cases is 1.

There is no upper limit to the excess kurtosis and it may be infinite.

Now the parameter m only controls the kurtosis of the distribution.

Skewness and kurtosis are well controlled by the parameters of the distribution.

The excess kurtosis may be either known beforehand for certain distributions, or estimated from the data.

These tests of normality can be applied if one faces kurtosis risk, for instance.

Unfortunately, the notation for kurtosis has not been standardized.

Expressions for the mean, variance, skewness and kurtosis can be derived from this.

It resembles the normal distribution in shape but has heavier tails (higher kurtosis).

An example of the online algorithm for kurtosis implemented as described is:

Kurtosis risk is commonly referred to as "fat tail" risk.

The beta rectangular exhibited larger variance and smaller kurtosis by comparison.

The magic word is "kurtosis," a k a "fat tails."

Another reason can be seen by looking at the formula for the kurtosis of the sum of random variables.

The shape of the distribution may also be described via indices such as skewness and kurtosis.

The variance, skewness, and excess kurtosis can be calculated from these raw moments.

Explicit expressions for the skewness and kurtosis are lengthy.

One can reparameterize with , where is the kurtosis as defined above.

Outliers that cannot be readily explained demand special attention - see kurtosis risk and black swan theory.

Kurtosis has also been used to distinguish the seismic signal generated by a person's footsteps from other signals.

The kurtosis excess may also be written as: