Syntax

Description

X = evinv(P,mu,sigma)returns the inverse cumulative distribution function (cdf) for a type 1 extreme value distribution with location parametermuand scale parametersigma, evaluated at the values inP.P,mu, andsigmacan 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 formuandsigmaare0and1, respectively.

[X,XLO,XUP] = evinv(P,mu,sigma,pcov,alpha)produces confidence bounds forXwhen the input parametersmuandsigmaare estimates.pcovis the covariance matrix of the estimated parameters.alphais a scalar that specifies 100(1 –alpha)% confidence bounds for the estimated parameters, and has a default value of 0.05.XLOandXUPare arrays of the same size asXcontaining the lower and upper confidence bounds.

The functionevinvcomputes confidence bounds forPusing a normal approximation to the distribution of the estimate

whereqis thePth quantile from an extreme value distribution with parametersμ= 0andσ = 1. The computed bounds give approximately the desired confidence level when you estimatemu,sigma, andpcovfrom 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 negatingX. SeeExtreme Value Distributionfor more details. Ifxhas a Weibull distribution, thenX= log(x) has the type 1 extreme value distribution.

Extended Capabilities

版本历史

See Also

icdf|evcdf|evpdf|evstat|evfit|evlike|evrnd