pdfaep4 {lmomco} | R Documentation |
Probability Density Function of the 4-Parameter Asymmetric Exponential Power Distribution
Description
This function computes the probability density of the 4-parameter Asymmetric Exponential Power distribution given parameters (\xi
,
\alpha
, \kappa
, and h
) computed by paraep4
. The probability density function is
f(x) = \frac{\kappa\,h}{\alpha(1+\kappa^2)\,\Gamma(1/h)}\,
\mathrm{exp}\left( -\left[\kappa^{ \mathrm{sign}(x-\xi)}\left(\frac{|x-\xi|}{\alpha}\right)\,\right]^h \right)
where f(x)
is the probability density for quantile x
,
\xi
is a location parameter, \alpha
is a scale parameter,
\kappa
is a shape parameter, and h
is another shape parameter. The range is -\infty < x < \infty
. If the \tau_3
of the distribution is zero (symmetrical), then the distribution is known as the Exponential Power (see lmrdia46
).
Usage
pdfaep4(x, para, paracheck=TRUE)
Arguments
x |
A real value vector. |
para |
|
paracheck |
A logical controlling whether the parameters and checked for validity. |
Value
Probability density (f
) for x
.
Author(s)
W.H. Asquith
References
Asquith, W.H., 2014, Parameter estimation for the 4-parameter asymmetric exponential power distribution by the method of L-moments using R: Computational Statistics and Data Analysis, v. 71, pp. 955–970.
Delicado, P., and Goria, M.N., 2008, A small sample comparison of maximum likelihood, moments and L-moments methods for the asymmetric exponential power distribution: Computational Statistics and Data Analysis, v. 52, no. 3, pp. 1661–1673.
See Also
cdfaep4
, quaaep4
, lmomaep4
, paraep4
Examples
aep4 <- vec2par(c(1000,15000,0.5,0.4), type='aep4');
F <- nonexceeds();
x <- quaaep4(F,aep4);
check.pdf(pdfaep4,aep4,plot=TRUE);
## Not run:
delx <- .01;
x <- seq(-10,10, by=delx);
K <- 3;
PAR <- list(para=c(0,1, K, 0.5), type="aep4");
plot(x,pdfaep4(x, PAR), type="n",
ylab="PROBABILITY DENSITY",
ylim=c(0,0.6), xlim=range(x));
lines(x,pdfaep4(x,PAR), lwd=2);
PAR <- list(para=c(0,1, K, 1), type="aep4");
lines(x,pdfaep4(x, PAR), lty=2, lwd=2);
PAR <- list(para=c(0,1, K, 2), type="aep4");
lines(x,pdfaep4(x, PAR), lty=3, lwd=2);
PAR <- list(para=c(0,1, K, 4), type="aep4");
lines(x,pdfaep4(x, PAR), lty=4, lwd=2);
## End(Not run)