Skewness

Explained:

skewness


Skewness is a parameter that describes asymmetry in a random variable’s probability distribution. Both probability density functions (PDFs) in Exhibit 1 have the same mean and standard deviation. The one on the left is positively skewed. The one on the right is negatively skewed.

Positive vs. Negative Skewness
Exhibit 1

These graphs illustrate the notion of skewness. Both PDFs have the same expectation and variance. The one on the left is positively skewed. The one on the right is negatively skewed.

The skewness of a random variable X is denoted or skew(X). It is defined as:

[1]

where and are the mean and standard deviation of X. As one might expect, the formula takes on a positive value if X is positively skewed and a negative value if X is negatively skewed.

 

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chi-squared distribution If you square a normal random variable, the result is a chi-squared random variable.

Cornish-Fisher expansion A formula for approximating quintiles of a random variable based only on its first few cumulants.

expected value A parameter describing the "center of gravity" of a distribution.

joint normal distribution A multivariate distribution with normal marginal distributions.

kurtosis A parameter describing the peakedness and tails of a distribution.

lognormal distribution A random variable is lognormal if its logarithm is normal.

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quantile A notion from probability that can be used as a parameter.

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Related Books

Evans, Hastings and Peacock (2000) is a handy reference with detailed information on numerous probability distributions, including formulas for the skewness of each.

Statistical Distributions

M. Evans, N. Hastings, B. Peacock

quality

 

technical  

2000

 

Related Papers

Holton, Glyn A. (2003). Negatively skewed trading strategies, Derivatives Week, October 20, 8–9.

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