This function computes the cumulative probability or nonexceedance probability of the Weibull distribution given parameters (parwei
. The cumulative distribution function is
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 relations between the Generalized Extreme Value parameters (
In R, the cumulative 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$para[2])
. For the current implementation for this package, the reversed Generalized Extreme Value distribution is used 1-cdfgev(-x,para)
.
cdfwei(x, para)
Nonexceedance probability (
A real value vector.
The parameters from parwei
or vec2par
.
W.H. Asquith
Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.
pdfwei
, quawei
, lmomwei
, parwei
# Evaluate Weibull deployed here and within R (pweibull)
lmr <- lmoms(c(123,34,4,654,37,78))
WEI <- parwei(lmr)
F1 <- cdfwei(50,WEI)
F2 <- pweibull(50+WEI$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 overlaps previous
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