VGAM (version 1.0-5)

Frechet: The Frechet Distribution

Description

Density, distribution function, quantile function and random generation for the three parameter Frechet distribution.

Usage

dfrechet(x, location = 0, scale = 1, shape, log = FALSE)
pfrechet(q, location = 0, scale = 1, shape,
         lower.tail = TRUE, log.p = FALSE)
qfrechet(p, location = 0, scale = 1, shape,
         lower.tail = TRUE, log.p = FALSE)
rfrechet(n, location = 0, scale = 1, shape)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Passed into runif.

location, scale, shape

the location parameter \(a\), scale parameter \(b\), and shape parameter \(s\).

log

Logical. If log = TRUE then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in punif or qunif.

Value

dfrechet gives the density, pfrechet gives the distribution function, qfrechet gives the quantile function, and rfrechet generates random deviates.

Details

See frechet, the VGAM family function for estimating the 2 parameters (without location parameter) by maximum likelihood estimation, for the formula of the probability density function and range restrictions on the parameters.

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

frechet.

Examples

# NOT RUN {
 shape <- 5
x <- seq(-0.1, 3.5, length = 401)
plot(x, dfrechet(x, shape = shape), type = "l", ylab = "", las = 1,
     main = "Frechet density divided into 10 equal areas; orange = cdf")
abline(h = 0, col = "blue", lty = 2)
qq <- qfrechet(seq(0.1, 0.9, by = 0.1), shape = shape)
lines(qq, dfrechet(qq, shape = shape), col = "purple", lty = 3, type = "h")
lines(x, pfrechet(q = x, shape = shape), col = "orange")
# }