gevfit
Estimate parameters and confidence intervals for the generalized extreme value (GEV) distribution.
paramhat = gevfit (x) returns the maximum likelihood
estimates of the parameters of the GEV distribution given the data in
x. paramhat(1) is the shape parameter, k, and
paramhat(2) is the scale parameter, sigma, and
paramhat(3) is the location parameter, mu.
[paramhat, paramci] = gevfit (x) returns the 95%
confidence intervals for the parameter estimates.
[…] = gevfit (x, alpha) also returns the
100 * (1 - alpha) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.
[…] = gevfit (…, options) specifies control
parameters for the iterative algorithm used to compute the maximum likelihood
estimates. options is a structure with the following field and its
default value:
options.Display = "off"
options.MaxFunEvals = 1000
options.MaxIter = 500
options.TolX = 1e-6
When k < 0, the GEV is the type III extreme value distribution.
When k > 0, the GEV distribution is the type II, or Frechet,
extreme value distribution. If W has a Weibull distribution as
computed by the wblcdf function, then -W has a type III
extreme value distribution and 1/W has a type II extreme value
distribution. In the limit as k approaches 0, the GEV is the
mirror image of the type I extreme value distribution as computed by the
evcdf function.
The mean of the GEV distribution is not finite when k >= 1, and
the variance is not finite when k >= 1/2. The GEV distribution
has positive density only for values of x such that
k * (x - mu) / sigma > -1.
Further information about the generalized extreme value distribution can be found at https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution
See also: gevcdf, gevinv, gevpdf, gevrnd, gevlike, gevstat
Source Code: gevfit
## Sample 2 populations from 2 different exponential distibutions
rand ("seed", 1); # for reproducibility
r1 = gevrnd (-0.5, 1, 2, 5000, 1);
rand ("seed", 2); # for reproducibility
r2 = gevrnd (0, 1, -4, 5000, 1);
r = [r1, r2];
## Plot them normalized and fix their colors
hist (r, 50, 5);
h = findobj (gca, "Type", "patch");
set (h(1), "facecolor", "c");
set (h(2), "facecolor", "g");
hold on
## Estimate their k, sigma, and mu parameters
k_sigma_muA = gevfit (r(:,1));
k_sigma_muB = gevfit (r(:,2));
## Plot their estimated PDFs
x = [-10:0.5:20];
y = gevpdf (x, k_sigma_muA(1), k_sigma_muA(2), k_sigma_muA(3));
plot (x, y, "-pr");
y = gevpdf (x, k_sigma_muB(1), k_sigma_muB(2), k_sigma_muB(3));
plot (x, y, "-sg");
ylim ([0, 0.7])
xlim ([-7, 5])
legend ({"Normalized HIST of sample 1 with ξ=-0.5, σ=1, μ=2", ...
"Normalized HIST of sample 2 with ξ=0, σ=1, μ=-4",
sprintf("PDF for sample 1 with estimated ξ=%0.2f, σ=%0.2f, μ=%0.2f", ...
k_sigma_muA(1), k_sigma_muA(2), k_sigma_muA(3)), ...
sprintf("PDF for sample 3 with estimated ξ=%0.2f, σ=%0.2f, μ=%0.2f", ...
k_sigma_muB(1), k_sigma_muB(2), k_sigma_muB(3))})
title ("Two population samples from different exponential distibutions")
hold off
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