Generalized Extreme Value Distribution

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Description

These functions provide information about the generalized extreme value distribution with location parameter equal to m, dispersion equal to s, and family parameter equal to f: density, cumulative distribution, quantiles, log hazard, and random generation.

The generalized extreme value distribution has density

f(y) = y^(f-1) exp(y^f/f) (s/m) (exp(y^f/f)/m)^(s-1) exp(-(exp(y^f/f)/m)^s)/(1-I(f>0)+sign(f) exp(-m^-s))

where m is the location parameter of the distribution, s is the dispersion, f is the family parameter, I() is the indicator function, and y>0.

f=1 a truncated extreme value distribution.

Usage

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dgextval(y, s, m, f, log=FALSE)
pgextval(q, s, m, f)
qgextval(p, s, m, f)
rgextval(n, s, m, f)

Arguments

y

vector of responses.

q

vector of quantiles.

p

vector of probabilities

n

number of values to generate

m

vector of location parameters.

s

vector of dispersion parameters.

f

vector of family parameters.

log

if TRUE, log probabilities are supplied.

Author(s)

J.K. Lindsey

See Also

dweibull for the Weibull distribution.

Examples

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dgextval(1, 2, 1, 2)
pgextval(1, 2, 1, 2)
qgextval(0.82, 2, 1, 2)
rgextval(10, 2, 1, 2)

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