quawei {lmomco} | R Documentation |
This function computes the quantiles of the Weibull
distribution given parameters (zeta, β, and delta) of the
distribution computed by parwei
. The quantile function of the
distribution is
x(F) = β[- log(1-F)]^{1/delta} - zeta mbox{,}
where x(F) is the quantile for nonexceedance probability F, 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 distribution 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 quantile function of the Weibull distribution is qweibull
. Given a Weibull parameter object p
, the R syntax is qweibull(f, p$para[3], scale=p$para[2]) - p$para[1]
. For the current implementation for this package, the reversed Generalized Extreme Value distribution is used -quagev((1-f),para)
.
quawei(f, para)
f |
Nonexceedance probability (0 <= F <= 1). |
para |
The parameters from parwei or similar. |
Quantile value for nonexceedance probability F.
W.H. Asquith
Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.
# Evaluate Weibull deployed here and within R (qweibull) lmr <- lmom.ub(c(123,34,4,654,37,78)) WEI <- parwei(lmr) Q1 <- quawei(0.5,WEI) Q2 <- qweibull(0.5,shape=WEI$para[3],scale=WEI$para[2])-WEI$para[1] if(Q1 == Q2) 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(F,quawei(F,WEI)) lines(F,-quagev(1-F,GEV),col=2) # line over laps previous