Cauchy Distribution for the Probability Distribution Calculator

Density Function. The Cauchy distribution has the probability density function:

f(x) = 1/( q*p*{1+[(x- h)/q]2})

0 < q

where

h

is the location parameter (median)

q

is the scale parameter

p

is the constant Pi (3.14..)

Distribution Function. The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Cauchy distribution is:

F(x) = 1/2 + 1/p*arctan[(x-h)/q]

C. This field displays the current variate value for the Cauchy distribution. When you edit this value (either manually or with the microscrolls), Statistica computes the associated p-value for the specified parameters.

p. This field displays the p-value computed from the specified variate value and parameters or you can enter a desired p-value (either manually or edit the existing value with the microscrolls) and compute the critical value for the specified parameters.

Location, Scale. Specify here the location and scale parameters of the distribution, h and q, respectively. If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.