frechet: Frechet Distribution Family Function

Description Usage Arguments Details Value Warning Author(s) References See Also Examples

View source: R/family.extremes.R

Description

Maximum likelihood estimation of the 2-parameter Frechet distribution.

Usage

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frechet(location = 0, lscale = "loglink", lshape = logofflink(offset = -2),
        iscale = NULL, ishape = NULL, nsimEIM = 250, zero = NULL)

Arguments

location

Numeric. Location parameter. It is called a below.

lscale, lshape

Link functions for the parameters; see Links for more choices.

iscale, ishape, zero, nsimEIM

See CommonVGAMffArguments for information.

Details

The (3-parameter) Frechet distribution has a density function that can be written

f(y) = ((s*b) / (y-a)^2) * exp[-(b/(y-a))^s] * [b/(y-a)]^(s-1)

for y > a and scale parameter b > 0. The positive shape parameter is s. The cumulative distribution function is

F(y) = exp[-(b/(y-a))^s].

The mean of Y is a + b*gamma(1-1/s) for s > 1 (these are returned as the fitted values). The variance of Y is b^2 * [gamma(1 - 2/s) - gamma(1 - 1/s)^2] for s > 2.

Family frechet has a known, and log(b) and log(s - 2) are the default linear/additive predictors. The working weights are estimated by simulated Fisher scoring.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

Warning

Family function frechet may fail for low values of the shape parameter, e.g., near 2 or lower.

Author(s)

T. W. Yee

References

Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005). Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, NJ, USA: Wiley-Interscience.

See Also

rfrechet, gev.

Examples

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## Not run: 
set.seed(123)
fdata <- data.frame(y1 = rfrechet(nn <- 1000, shape = 2 + exp(1)))
with(fdata, hist(y1))
fit2 <- vglm(y1 ~ 1, frechet, data = fdata, trace = TRUE)
coef(fit2, matrix = TRUE)
Coef(fit2)
head(fitted(fit2))
with(fdata, mean(y1))
head(weights(fit2, type = "working"))
vcov(fit2)

## End(Not run)

Example output

Loading required package: stats4
Loading required package: splines
VGLM    linear loop  1 :  loglikelihood = -234.51152
VGLM    linear loop  2 :  loglikelihood = -142.3688
VGLM    linear loop  3 :  loglikelihood = -134.8156
VGLM    linear loop  4 :  loglikelihood = -134.77484
VGLM    linear loop  5 :  loglikelihood = -134.77482
VGLM    linear loop  6 :  loglikelihood = -134.77482
             loge(scale) logoff(shape, offset = -2)
(Intercept) -0.002031548                   1.013375
    scale     shape 
0.9979705 4.7548828 
         [,1]
[1,] 1.173629
[2,] 1.173629
[3,] 1.173629
[4,] 1.173629
[5,] 1.173629
[6,] 1.173629
[1] 1.171643
         [,1]      [,2]     [,3]
[1,] 22.60561 0.6056725 1.168047
[2,] 22.60561 0.6056725 1.168047
[3,] 22.60561 0.6056725 1.168047
[4,] 22.60561 0.6056725 1.168047
[5,] 22.60561 0.6056725 1.168047
[6,] 22.60561 0.6056725 1.168047
              (Intercept):1 (Intercept):2
(Intercept):1  4.913277e-05 -9.475318e-05
(Intercept):2 -9.475318e-05  1.833790e-03

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.