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## Excess Kurtosis of a Distribution

by QuantShare, 4071 days ago

In statistics, kurtosis measures the relative peakedness of a probability distribution compared with the normal distribution. This is why we also call it "excess kurtosis".

The higher the kurtosis value is, the sharper the distribution peak and the longer & fatter the tails are.
The lower the kurtosis value is, the rounder the distribution peak and the shorter & thinner the tails are.

- Mesokurtic or mesokurtotic refers to distributions with zero excess kurtosis. The normal distribution is an example of a mesokurtic distribution.
- Leptokurtic or leptokurtotic refers to distributions with positive excess kurtosis. Example: Student's t-distribution, Laplace distribution, Cauchy distribution, Exponential distribution, Rayleigh distribution and Poisson distribution.
- Platykurtic or platykurtotic refers to distributions with negative excess kurtosis. Examples: Raised cosine distribution, Bernoulli distribution and Uniform distributions,

The kurtosis indicator returns the excess kurtosis of the probability distribution of a time-series over the past N-bars.

Examples:
a = Kurtosis(close, 200);
plot(a, "");

The above formula plots, on a chart, the excess kurtosis of the close series for each bar and for the previous 200 trading days.

rule1 = Kurtosis(close, 200) == 0;

The above rule returns 1 on the bar where the probability distribution of the past 200 close prices is normal (Prices are normally distributed).

What is this?

 Type: Trading Indicator Object ID: 1045 Country: All Market: All Style: Technical Analysis

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