| Card {VGAM} | R Documentation |
Density, distribution function, quantile function and random generation for the cardioid distribution.
dcard(x, mu, rho) pcard(q, mu, rho) qcard(p, mu, rho, tolerance = 1e-07, maxits = 500) rcard(n, mu, rho, ...)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. Must be a single positive integer. |
mu, rho |
See cardioid for more information.
|
tolerance, maxits, ... |
The first two are control parameters for the algorithm
used to solve for the roots of a nonlinear system of equations;
tolerance controls for the accuracy and
maxits is the maximum number of iterations.
rcard calls qcard so the ... can be used
to vary the two arguments.
|
See cardioid, the VGAM family function
for estimating the two parameters by maximum likelihood estimation,
for the formula of the probability density function and other details.
dcard gives the density,
pcard gives the distribution function,
qcard gives the quantile function, and
rcard generates random deviates.
Convergence problems might occur with rcard.
Thomas W. Yee
## Not run:
mu = 4; rho = 0.4
x = seq(0, 2*pi, len=501)
plot(x, dcard(x, mu, rho), type="l", las=1, ylim=c(0,1), col="blue",
ylab=paste("[dp]card(mu=", mu, ", rho=", rho, ")"),
main="Blue is density, red is cumulative distribution function",
sub="Purple lines are the 10,20,...,90 percentiles")
lines(x, pcard(x, mu, rho), col="red")
probs = seq(0.1, 0.9, by=0.1)
Q = qcard(probs, mu, rho)
lines(Q, dcard(Q, mu, rho), col="purple", lty=3, type="h")
lines(Q, pcard(Q, mu, rho), col="purple", lty=3, type="h")
abline(h=c(0,probs,1), v=c(0,2*pi), col="purple", lty=3)
max(abs(pcard(Q, mu, rho) - probs)) # Should be 0
## End(Not run)