evcdf - Extreme value cumulative distribution function
Syntax
P = evcdf(X,mu,sigma)
[P,PLO,PUP] = evcdf(X,mu,sigma,pcov,alpha)
Description
P = evcdf(X,mu,sigma) computes the cumulative
distribution function (cdf) for the type 1 extreme value distribution,
with location parameter mu and scale parameter sigma,
at each of the values in X. X, mu,
and sigma can be vectors, matrices, or multidimensional
arrays that all have the same size. A scalar input is expanded to
a constant array of the same size as the other inputs. The default
values for mu and sigma are 0 and 1,
respectively.
[P,PLO,PUP] = evcdf(X,mu,sigma,pcov,alpha) produces
confidence bounds for P when the input parameters mu and sigma are
estimates. pcov is a 2-by-2 covariance matrix of
the estimated parameters. alpha has a default value
of 0.05, and specifies 100(1 - alpha)% confidence bounds. PLO and PUP are
arrays of the same size as P, containing the lower
and upper confidence bounds.
The function evcdf computes confidence bounds
for P using a normal approximation to the distribution
of the estimate
and then transforming those bounds to the scale of the output P.
The computed bounds give approximately the desired confidence level
when you estimate mu, sigma,
and pcov from large samples, but in smaller samples
other methods of computing the confidence bounds might be more accurate.
The type 1 extreme value distribution is also known as the Gumbel
distribution. The version used here is suitable for modeling minima;
the mirror image of this distribution can be used to model maxima
by negating X. See Extreme Value Distribution for more details. If x has
a Weibull distribution, then X = log(x)
has the type 1 extreme value distribution.
See Also
cdf, evpdf, evinv, evstat, evfit, evlike, evrnd
Extreme Value Distribution
 | end (qrandset) | | evfit |  |
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