lkhlmomco | R Documentation |
This function computes the Leimkuhler Curve for quantile function x(F)
(par2qua
, qlmomco
). The function is defined by Nair et al. (2013, p. 181) as
K(u) = 1 - \frac{1}{\mu}\int_0^{1-u} x(p)\; \mathrm{d}p\mbox{,}
where K(u)
is Leimkuhler curve for nonexceedance probability u
. The Leimkuhler curve is related to the Lorenz curve (L(u)
, lrzlmomco
) by
K(u) = 1-L(1-u)\mbox{,}
and related to the reversed residual mean quantile function (R(u)
, rrmlmomco
) and conditional mean (\mu
, cmlmomco
) for u=0
by
K(u) = \frac{1}{\mu} [\mu - (1-u)(x(1-u) - R(1-u))] \mbox{.}
lkhlmomco(f, para)
f |
Nonexceedance probability ( |
para |
The parameters from |
Leimkuhler curve value for F
.
W.H. Asquith
Nair, N.U., Sankaran, P.G., and Balakrishnan, N., 2013, Quantile-based reliability analysis: Springer, New York.
qlmomco
, lrzlmomco
# It is easiest to think about residual life as starting at the origin, units in days.
A <- vec2par(c(0.0, 2649, 2.11), type="gov") # so set lower bounds = 0.0
"afunc" <- function(u) { return(par2qua(u,A,paracheck=FALSE)) }
f <- 0.35 # All three computations report: Ku = 0.6413727
Ku1 <- 1 - 1/cmlmomco(f=0,A) * integrate(afunc,0,1-f)$value
Ku2 <- (cmlmomco(0,A) - (1-f)*(quagov(1-f,A) - rrmlmomco(1-f,A)))/cmlmomco(0,A)
Ku3 <- lkhlmomco(f, A)
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