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Cauchy Distribution

Statistical properties

mean | indeterminate
mode | a
standard deviation | indeterminate
variance | indeterminate
skewness | indeterminate

Probability density function (PDF)

1/(π b ((x - a)^2/b^2 + 1))

Plots of PDF for typical parameters

Plots of PDF for typical parameters

Cumulative distribution function (CDF)

P (X<=x) = (tan^(-1)((x - a)/b))/π + 1/2

Plots of CDF for typical parameters

Plots of CDF for typical parameters

Percentiles

10th | a - 3.07768 b
25th | a - b
50th | a
75th | a + b
90th | a + 3.07768 b

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