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Inversion of skewness
Skewed distributions can be inverted (or mirrored) by replacing in the mathematical expression of the cumulative distribution function (F) by its complement: F'=1-F, obtaining the complementary distribution function (also called survival function) that gives a mirror image. In this manner, a distribution that is skewed to the right is transformed into a distribution that is skewed to the left and vice versa.
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 * bgcolor="white" |Example. The F-expression of the positively skewed Gumbel distribution is: F=exp[-exp{-(X-u)/0.78s}], where u is the mode (i.e. the value occurring most frequently) and s is the standard deviation. The Gumbel distribution can be transformed using F'=1-exp[-exp{-(x-u)/0.78s}] . This transformation yields the inverse, mirrored, or complementary Gumbel distribution that may fit a data series obeying a negatively skewed distribution.
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