Function Reference: cauchycdf

statistics: p = cauchycdf (x, x0, gamma)
statistics: p = cauchycdf (x, x0, gamma, "upper")

Cauchy cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the Cauchy distribution with location parameter x0 and scale parameter gamma. The size of p is the common size of x, x0, and gamma. A scalar input functions as a constant matrix of the same size as the other inputs.

p = cauchycdf (x, x0, gamma, "upper") computes the upper tail probability of the Cauchy distribution with parameters x0 and gamma, at the values in x.

Further information about the Cauchy distribution can be found at https://en.wikipedia.org/wiki/Cauchy_distribution

See also: cauchyinv, cauchypdf, cauchyrnd

Source Code: cauchycdf

Example: 1

  

 ## Plot various CDFs from the Cauchy distribution
 x = -5:0.01:5;
 p1 = cauchycdf (x, 0, 0.5);
 p2 = cauchycdf (x, 0, 1);
 p3 = cauchycdf (x, 0, 2);
 p4 = cauchycdf (x, -2, 1);
 plot (x, p1, "-b", x, p2, "-g", x, p3, "-r", x, p4, "-c")
 grid on
 xlim ([-5, 5])
 legend ({"x0 = 0, γ = 0.5", "x0 = 0, γ = 1", ...
          "x0 = 0, γ = 2", "x0 = -2, γ = 1"}, "location", "southeast")
 title ("Cauchy CDF")
 xlabel ("values in x")
 ylabel ("probability")
plotted figure