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## Skewness of a Distribution

by QuantShare, 4615 days ago

A basic task in statistical analysis of a probability distribution consists of measuring its peakedness and asymmetry. Kurtosis measures peakedness of a distribution, while Skew measures asymmetry.

Kurtosis function is available here: Excess Kurtosis of a Distribution.

A normal distribution is symmetric, that is it looks the same to the right and the left of the center point, and thus its skewness is equal to zero.

A positive skew indicates that the right tail of the distribution is longer than the left tail and that most population values belong to the left part.
A negative skew indicates that the left tail is longer and that most values belong to the right part.

Example:
a = Skew(perf(close, 1), 100);
plot(a, "");

This formula measures the skewness of the probability distribution of the previous 100 one-bar returns.

The distribution is said to be right-skewed if it has a positive skew. This also means that there are more negative daily returns than positive ones. However, since the right tail is longer, highest daily returns are more likely to be positive.
It is left-skewed if it has a negative skew and this indicates that there are more positive daily returns than negative ones. Highest daily returns are more likely to be negative.

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 Type: Trading Indicator Object ID: 1046 Country: All Market: All Style: Technical Analysis

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