Function Reference: evcdf

statistics: p = evcdf (x)
statistics: p = evcdf (x, mu)
statistics: p = evcdf (x, mu, sigma)
statistics: p = evcdf (…, "upper")
statistics: [p, plo, pup] = evcdf (x, mu, sigma, pcov)
statistics: [p, plo, pup] = evcdf (x, mu, sigma, pcov, alpha)
statistics: [p, plo, pup] = evcdf (…, "upper")

Extreme value cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the type 1 extreme values CDF at x of the normal distribution with location parameter mu and scale parameter sigma. The size of p is the common size of x, mu and sigma. A scalar input functions as a constant matrix of the same size as the other inputs.

Default values are mu = 0, sigma = 1.

When called with three output arguments, [p, plo, pup] it computes the confidence bounds for p when the input parameters mu and sigma are estimates. In such case, pcov, a 2-by-2 matrix containing the covariance matrix of the estimated parameters, is necessary. 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 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. If y has a Weibull distribution, then x = log (y) has the type 1 extreme value distribution.

[…] = evcdf (…, "upper") computes the upper tail probability of the extreme value distribution.

See also: evinv, evpdf, evrnd, evfit, evlike, evstat

Source Code: evcdf