Extreme value cumulative distribution function
p = evcdf(x,mu,sigma)
[p,plo,pup] = evcdf(x,mu,sigma,pcov,alpha)
[p,plo,pup] = evcdf(___,'upper')
p = evcdf(x,mu,sigma) returns the cumulative
distribution function (cdf) for the type 1 extreme value distribution,
with location parameter
mu and scale parameter
at each of the values in
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
[p,plo,pup] = evcdf(x,mu,sigma,pcov,alpha) returns
confidence bounds for
p when the input parameters
pcov is a 2-by-2 covariance matrix of
the estimated parameters.
alpha has a default value
0.05, and specifies
100(1 - alpha)% confidence bounds.
arrays of the same size as
p, containing the lower
and upper confidence bounds.
[p,plo,pup] = evcdf(___,'upper') returns
the complement of the type 1 extreme value distribution cdf at each
x, using an algorithm that more accurately
computes the extreme upper tail probabilities. You can use the
with any of the previous syntaxes.
evcdf computes confidence bounds
P using a normal approximation to the distribution
of the estimate
and then transforming those bounds to the scale of the output
The computed bounds give approximately the desired confidence level
when you estimate
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
X and subtracting the resulting distribution
1. See Extreme Value Distribution for more details. If x has
a Weibull distribution, then X = log(x)
has the type 1 extreme value distribution.