### Function Reference: `gumbelpdf`

statistics: y = gumbelpdf (x)
statistics: y = gumbelpdf (x, mu)
statistics: y = gumbelpdf (x, mu, beta)

Gumbel probability density function (PDF).

For each element of x, compute the probability density function (PDF) 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 y 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.

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 iCDF, `evpdf`.

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

See also: gumbelcdf, gumbelinv, gumbelrnd, gumbelfit, gumbellike, gumbelstat, evpdf

Source Code: gumbelpdf

### Example: 1

     ## Plot various PDFs from the Extreme value distribution
     x = -5:0.001:20;
     y1 = gumbelpdf (x, 0.5, 2);
     y2 = gumbelpdf (x, 1.0, 2);
     y3 = gumbelpdf (x, 1.5, 3);
     y4 = gumbelpdf (x, 3.0, 4);
     plot (x, y1, "-b", x, y2, "-g", x, y3, "-r", x, y4, "-c")
     grid on
     ylim ([0, 0.2])
     legend ({"μ = 0.5, β = 2", "μ = 1.0, β = 2", ...
              "μ = 1.5, β = 3", "μ = 3.0, β = 4"}, "location", "northeast")
     title ("Extreme value PDF")
     xlabel ("values in x")
     ylabel ("density")