pdfwei {lmomco} | R Documentation |
This function computes the probability density of the Weibull distribution given parameters (zeta, β, and delta) of the distribution computed by parwei
. The probability density function of the distribution is
f(x) =
where f(x) is the probability density for quantile x, zeta is a location parameter, β is a scale parameter, and delta is a shape parameter.
The Weibull distribution is a reverse Generalized Extreme Value distribution. As result, the Generalized Extreme Value algorithms are used for implementation of the Weibull in this package. The relation between the Generalized Extreme Value parameters (xi, α, and kappa) is
kappa = 1/delta mbox{,}
α = β/delta mbox{, and}
xi = zeta - β mbox{.}
These relations are taken from Hosking and Wallis (1997).
In R the probability distribution function of the Weibull distribution is pweibull
. Given a Weibull parameter object para
, the R syntax is pweibull(x+para$para[1], para$para[3], scale=para$para[2])
. For the current implementation for this package, the reversed Generalized Extreme Value distribution is used pdfgev(-x,para)
.
pdfwei(x, para)
x |
A real value. |
para |
The parameters from parwei or similar. |
Probability density (f) for x.
W.H. Asquith
Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.
# Evaluate Weibull deployed here and within R (pweibull) lmr <- lmom.ub(c(123,34,4,654,37,78)) WEI <- parwei(lmr) F1 <- cdfwei(50,WEI) F2 <- pweibull(50+WEI$para[1],shape=WEI$para[3],scale=WEI$para[2]) if(F1 == F2) EQUAL <- TRUE # The Weibull is a reversed generalized extreme value Q <- sort(rlmomco(34,WEI)) # generate Weibull sample lm1 <- lmoms(Q) # regular L-moments lm2 <- lmoms(-Q) # L-moment of negated (reversed) data WEI <- parwei(lm1) # parameters of Weibull GEV <- pargev(lm2) # parameters of GEV F <- nonexceeds() # Get a vector of nonexceedance probs plot(pp(Q),Q) lines(cdfwei(Q,WEI),Q,lwd=5,col=8) lines(1-cdfgev(-Q,GEV),Q,col=2) # line over laps previous