The Frechet Distribution

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.

References

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

Author

T. W. Yee and Kai Huang

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.

Examples

if (FALSE)  shape <- 5
x <- seq(-0.1, 3.5, length = 401)
plot(x, dfrechet(x, shape = shape), type = "l", ylab = "",
  main = "Frechet density divided into 10 equal areas",
  sub = "Orange = CDF", las = 1)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'y' in selecting a method for function 'plot': object 'shape' not found
abline(h = 0, col = "blue", lty = 2)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
qq <- qfrechet(seq(0.1, 0.9, by = 0.1), shape = shape)
#> Error: object 'shape' not found
lines(qq, dfrechet(qq, shape = shape), col = 2, lty = 2, type = "h")
#> Error: object 'qq' not found
lines(x, pfrechet(q = x, shape = shape), col = "orange")
#> Error: object 'shape' not found
 # \dontrun{}