evinv
Extreme value inverse cumulative distribution function
Syntax
X = evinv(P,mu,sigma)
[X,XLO,XUP] = evinv(P,mu,sigma,pcov,alpha)
Description
X = evinv(P,mu,sigma) returns the inverse
cumulative distribution function (cdf) for a type 1 extreme value
distribution with location parameter mu and scale
parameter sigma, evaluated at the values in P. P, 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.
[X,XLO,XUP] = evinv(P,mu,sigma,pcov,alpha) produces
confidence bounds for X when the input parameters mu and sigma are
estimates. pcov is the covariance matrix of the
estimated parameters. alpha is a scalar that specifies
100(1 – alpha)% confidence bounds for the
estimated parameters, and has a default value of 0.05. XLO and XUP are
arrays of the same size as X containing the lower
and upper confidence bounds.
The function evinv computes confidence bounds
for P using a normal approximation to the distribution
of the estimate
where q is the Pth quantile
from an extreme value distribution with parameters μ
= 0 and σ = 1. 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.
Extended Capabilities
Version History
Introduced before R2006a
