Cauchy distribution Probabilities
Calculator of Cauchy distribution : probabilities, density function (PDF) and cumulative density function (CDF).
Cauchy Distribution formulas
X : a random variable following a Cauchy distribution
t : location parameter
s : scale parameter (s > 0)
Probability Density Function (PDF)
`f(x) = 1/pi*(s/((x-t)^2+s^2))`
Cumulative distribution function (CDF)
`F(x) = \int_-oo^x f(t)\ dt`
`F(x) = 1/2+1/pi*arctan((x-t)/s)`
Probabilities
Probability that X is greater than a :
`P(X > a) = 1 - F(a) = 1/2-1/pi*arctan((a-t)/s)`
Probability that X is less than b :
`P(X < b) = F(b) = 1/2+1/pi*arctan((b-t)/s)`
Probability that X lies between a and b :
`P(a < X < b) = F(b) - F(a)`
See also
Inverse Cauchy distribution
Cauchy distribution Chart
Statistics Calculators