User:Asitgoes
Appearance
When absolutely sure, it is difficult to rise above oneself.
[edit]Variation in random samples
[edit]![](http://upload.wikimedia.org/wikipedia/commons/thumb/5/51/SampleFreqCurves.tif/lossy-page1-500px-SampleFreqCurves.tif.jpg)
Reference
[edit]- ^ Benson, M.A. 1960. Characteristics of frequency curves based on a theoretical 1000 year record. In: T.Dalrymple (Ed.), Flood frequency analysis. U.S. Geological Survey Water Supply Paper, 1543-A, pp. 51-71.
Binomial confidence belts
[edit]- Different picture formats
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jpg file
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tif file, less clear
Probability paper
[edit]- Plotting on probability paper
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Plot of data on normal probability paper
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Plot of data and confidence belt on normal probability paper
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Plot of data and confidence belt on Gumbel probability paper
Inversion of skewness
[edit]![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Gumbel_distribution_and_Gumbel_mirrored.png/220px-Gumbel_distribution_and_Gumbel_mirrored.png)
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.
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.