page_title: Probability distribution fitting
section_title: Inversion of skewness
hierarchical_section_title: Probability distribution fitting / Inversion of skewness
caption_attribution_description: English: Gumbel probability distribution skew to right and Gumbel mirrored skew to left
context_page_description: Probability distribution fitting or simply distribution fitting is the fitting of a probability distribution to a series of data concerning the repeated measurement of a variable phenomenon.
  The aim of distribution fitting is to predict the probability or to forecast the frequency of occurrence of the magnitude of the phenomenon in a certain interval.
  There are many probability distributions of which some can be fitted more closely to the observed frequency of the data than others, depending on the characteristics of the phenomenon and of the distribution. The distribution giving a close fit is supposed to lead to good predictions.
  In distribution fitting, therefore, one needs to select a distribution that suits the data well.
context_section_description: 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.
  The technique of skewness inversion increases the number of probability distributions available for distribution fitting and enlarges the distribution fitting opportunities.
caption: (A) Gumbel probability distribution skew to right and (B) Gumbel mirrored skew to left
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