Function Reference: gumbelcdf

statistics: p = gumbelcdf (x)
statistics: p = gumbelcdf (x, mu)
statistics: p = gumbelcdf (x, mu, beta)
statistics: p = gumbelcdf (…, "upper")
statistics: [p, plo, pup] = gumbelcdf (x, mu, beta, pcov)
statistics: [p, plo, pup] = gumbelcdf (x, mu, beta, pcov, alpha)
statistics: [p, plo, pup] = gumbelcdf (…, "upper")

Gumbel cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the Gumbel distribution (also known as the extreme value or the type I generalized extreme value distribution) with location parameter mu and scale parameter beta. The size of p is the common size of x, mu and beta. A scalar input functions as a constant matrix of the same size as the other inputs.

Default values are mu = 0 and beta = 1.

When called with three output arguments, i.e. [p, plo, pup], gumbelcdf computes the confidence bounds for p when the input parameters mu and beta are estimates. In such case, pcov, a 2×2 matrix containing the covariance matrix of the estimated parameters, is necessary. Optionally, alpha, which has a default value of 0.05, specifies the 100 * (1 - alpha) percent confidence bounds. plo and pup are arrays of the same size as p containing the lower and upper confidence bounds.

[…] = gumbelcdf (…, "upper") computes the upper tail probability of the Gumbel distribution with parameters mu and beta, at the values in x.

The Gumbel distribution is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. This version is suitable for modeling maxima. For modeling minima, use the alternative extreme value CDF, evcdf.

[…] = gumbelcdf (…, "upper") computes the upper tail probability of the extreme value (Gumbel) distribution.

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

See also: gumbelinv, gumbelpdf, gumbelrnd, gumbelfit, gumbellike, gumbelstat, evcdf

Source Code: gumbelcdf

Example: 1

  

 ## Plot various CDFs from the Gumbel distribution
 x = -5:0.01:20;
 p1 = gumbelcdf (x, 0.5, 2);
 p2 = gumbelcdf (x, 1.0, 2);
 p3 = gumbelcdf (x, 1.5, 3);
 p4 = gumbelcdf (x, 3.0, 4);
 plot (x, p1, "-b", x, p2, "-g", x, p3, "-r", x, p4, "-c")
 grid on
 legend ({"μ = 0.5, β = 2", "μ = 1.0, β = 2", ...
          "μ = 1.5, β = 3", "μ = 3.0, β = 4"}, "location", "southeast")
 title ("Gumbel CDF")
 xlabel ("values in x")
 ylabel ("probability")
plotted figure