lmomgov {lmomco} | R Documentation |
L-moments of the Govindarajulu Distribution
Description
This function estimates the L-moments of the Govindarajulu distribution given the parameters (\xi
, \alpha
, and \beta
) from pargov
. The L-moments in terms of the parameters are
\lambda_1 = \xi + \frac{2\alpha}{\beta+2} \mbox{,}
\lambda_2 = \frac{2\alpha\beta}{(\beta+2)(\beta+3)} \mbox{,}
\tau_3 = \frac{\beta-2}{\beta+4} \mbox{, and}
\tau_4 = \frac{(\beta-5)(\beta-1)}{(\beta+4)(\beta+5)} \mbox{.}
The limits of \tau_3
are (-1/2, 1)
for \beta \rightarrow 0
and \beta \rightarrow \infty
.
Usage
lmomgov(para)
Arguments
para |
The parameters of the distribution. |
Value
An R list is returned.
lambdas |
Vector of the L-moments. First element is
|
ratios |
Vector of the L-moment ratios. Second element is
|
trim |
Level of symmetrical trimming used in the computation, which is |
leftrim |
Level of left-tail trimming used in the computation, which is |
rightrim |
Level of right-tail trimming used in the computation, which is |
source |
An attribute identifying the computational source of the L-moments: “lmomgov”. |
Author(s)
W.H. Asquith
References
Gilchrist, W.G., 2000, Statistical modelling with quantile functions: Chapman and Hall/CRC, Boca Raton.
Nair, N.U., Sankaran, P.G., Balakrishnan, N., 2013, Quantile-based reliability analysis: Springer, New York.
Nair, N.U., Sankaran, P.G., and Vineshkumar, B., 2012, The Govindarajulu distribution—Some Properties and applications: Communications in Statistics, Theory and Methods, v. 41, no. 24, pp. 4391–4406.
See Also
pargov
, cdfgov
, pdfgov
, quagov
Examples
lmr <- lmoms(c(123,34,4,654,37,78))
lmorph(lmr)
lmomgov(pargov(lmr))
## Not run:
Bs <- exp(seq(log(.01),log(10000),by=.05))
T3 <- (Bs-2)/(Bs+4)
T4 <- (Bs-5)*(Bs-1)/((Bs+4)*(Bs+5))
plotlmrdia(lmrdia(), autolegend=TRUE)
points(T3, T4)
T3s <- c(-0.5,T3,1)
T4s <- c(0.25,T4,1)
the.lm <- lm(T4s~T3s+I(T3s^2)+I(T3s^3)+I(T3s^4)+I(T3s^5))
lines(T3s, predict(the.lm), col=2)
max(residuals(the.lm))
summary(the.lm)
## End(Not run)