Weibull distribution
Distribution function and quantile function of the Weibull distribution.
cdfwei(x, para = c(0, 1, 1)) quawei(f, para = c(0, 1, 1))
x |
Vector of quantiles. |
f |
Vector of probabilities. |
para |
Numeric vector containing the parameters of the distribution, in the order zeta, beta, delta (location, scale, shape). |
The Weibull distribution with location parameter zeta, scale parameter beta and shape parameter δ has distribution function
F(x) = 1 - exp[ - { (x - zeta) /beta }^delta ]
for x>zeta.
cdfwei gives the distribution function;
quawei gives the quantile function.
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
distribution functions pnorm, qnorm, etc.
cdfgev for the generalized extreme-value distribution,
of which the Weibull (reflected through the origin) is a special case.
# Random sample from a 2-parameter Weibull distribution # with scale parameter 2 and shape parameter 1.5. quawei(runif(100), c(0,2,1.5)) # Illustrate the relation between Weibull and GEV distributions. # weifit() fits a Weibull distribution to data and returns # quantiles of the fitted distribution # gevfit() fits a Weibull distribution as a "reverse GEV", # i.e. fits a GEV distribution to the negated data, # then computes negated quantiles weifit <- function(qval, x) quawei(qval, pelwei(samlmu(x))) gevfit <- function(qval, x) -quagev(1-qval, pelgev(samlmu(-x))) # Compare on Ozone data data(airquality) weifit(c(0.2,0.5,0.8), airquality$Ozone) gevfit(c(0.2,0.5,0.8), airquality$Ozone)
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