pystra.distributions.gev.GEVmax

class GEVmax(name, mean, stdv, shape, input_type=None, startpoint=None)

Bases: Distribution

Generalized Extreme Value (GEV) distribution for maxima.

This distribution unifies the different types of extreme value distributions: Gumbel (Type I), Fréchet (Type II), and Weibull (Type III).

Arguments:

• name (str): Name of the random variable

• mean (float): Mean

• stdv (float): Standard deviation

• shape (float): Shape parameter. shape < 0.0 is Weibull, shape > 0 is Frechet.

• input_type (any): Change meaning of mean and stdv

• startpoint (float): Start point for seach

Raises:

• ValueError: If shape is greater than or equal to 0.5

Notes:

• The shape parameter shape must be less than 0.5 for finite variance.

• shape < 0 is the Weibull case, shape = 0 is the Gumbel case, and shape > 0 is the Fréchet case.

• This distribution is to model maxima.

Methods

cdf	Cumulative distribution function
getMean
getName
getStartPoint
getStdv
jacobian	Compute the Jacobian
pdf	Probability density function
plot	Plots the PDF of the distribution
ppf	Inverse cumulative distribution function
sample	Return a sample of the distribution of length n
setStartPoint
set_location
set_scale
u_to_x	Transformation from u to x
x_to_u	Transformation from x to u

Attributes

std_normal

cdf(x)

Cumulative distribution function

jacobian(u, x)

Compute the Jacobian

pdf(x)

Probability density function

plot(ax=None, **kwargs)

Plots the PDF of the distribution

ppf(u)

Inverse cumulative distribution function

sample(n=1000)

Return a sample of the distribution of length n

u_to_x(u)

Transformation from u to x

x_to_u(x)

Transformation from x to u