cdfCauchy#

Purpose#

Computes the cumulative distribution function for the Cauchy distribution.

Format#

p = cdfCauchy(x, loc, scale)#

Parameters:

x (NxK matrix, Nx1 vector or scalar.) – Values at which to evaluate the Cauchy cdf.
loc (NxK matrix, Nx1 vector or scalar) – Location parameter. ExE conformable with x.
scale (NxK matrix, Nx1 vector or scalar) – Scale parameter. ExE conformable with x. \(scale > 0\)

Returns:

p (NxK matrix, Nx1 vector or scalar) – Each element in p is the Cauchy cdf value evaluated at the corresponding element in x.

Examples#

// Set seed for repeatable random numbers
rndseed 777;

// Values
x = rndn(10, 1);

// Cauchy distribution parameters
loc = 2;
scale = 0.75;

// Call cdfCauchy
p = cdfCauchy(x, loc, scale);
print "X~p =" x~p;

After running the above code,

X~p =
  0.5242   0.1497
  1.3741   0.2786
 -2.6114   0.0513
  0.6770   0.1642
 -0.3000   0.1003
  1.8822   0.4504
  1.1114   0.2231
 -1.2123   0.0730
  0.2336   0.1278
  1.9085   0.4614

Remarks#

The cumulative distribution function for the Cauchy distribution is defined as:

\[\frac{1}{2} + \frac{1}{\pi} arctan(\frac{x−a}{b})\]

where A is the location parameter and B is the scale parameter.