Function Reference: gpcdf

statistics: p = gpcdf (x, k, sigma, theta)
statistics: p = gpcdf (x, k, sigma, theta, "upper")

Generalized Pareto cumulative distribution function (CDF).

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

[…] = gpcdf(x, k, sigma, theta, "upper") computes the upper tail probability of the generalized Pareto distribution with parameters k, sigma, and theta, at the values in x.

When k = 0 and theta = 0, the Generalized Pareto is equivalent to the exponential distribution. When k > 0 and theta = k / k the Generalized Pareto is equivalent τπ the Pareto distribution. The mean of the Generalized Pareto is not finite when k >= 1 and the variance is not finite when k >= 1/2. When k >= 0, the Generalized Pareto has positive density for x > theta, or, when theta < 0, for 0 <= (x - theta) / sigma <= -1 / k.

Further information about the generalized Pareto distribution can be found at https://en.wikipedia.org/wiki/Generalized_Pareto_distribution

See also: gpinv, gppdf, gprnd, gpfit, gplike, gpstat

Source Code: gpcdf

Example: 1

  

 ## Plot various CDFs from the generalized Pareto distribution
 x = 0:0.001:5;
 p1 = gpcdf (x, 1, 1, 0);
 p2 = gpcdf (x, 5, 1, 0);
 p3 = gpcdf (x, 20, 1, 0);
 p4 = gpcdf (x, 1, 2, 0);
 p5 = gpcdf (x, 5, 2, 0);
 p6 = gpcdf (x, 20, 2, 0);
 plot (x, p1, "-b", x, p2, "-g", x, p3, "-r", ...
       x, p4, "-c", x, p5, "-m", x, p6, "-k")
 grid on
 xlim ([0, 5])
 legend ({"k = 1, σ = 1, θ = 0", "k = 5, σ = 1, θ = 0", ...
          "k = 20, σ = 1, θ = 0", "k = 1, σ = 2, θ = 0", ...
          "k = 5, σ = 2, θ = 0", "k = 20, σ = 2, θ = 0"}, ...
         "location", "northwest")
 title ("Generalized Pareto CDF")
 xlabel ("values in x")
 ylabel ("probability")
plotted figure