Cardioid Distribution
Density, distribution function, quantile function and random generation for the cardioid distribution.
dcard(x, mu, rho, log = FALSE)
pcard(q, mu, rho, lower.tail = TRUE, log.p = FALSE)
qcard(p, mu, rho, tolerance = 1e-07, maxits = 500,
lower.tail = TRUE, log.p = FALSE)
rcard(n, mu, rho, ...)x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Same as in |
mu, rho |
See |
tolerance, maxits, ... |
The first two are control parameters for the algorithm
used to solve for the roots of a nonlinear system of equations;
|
log |
Logical.
If |
lower.tail, log.p |
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 and Kai Huang
## 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, orange is cumulative distribution function",
sub = "Purple lines are the 10,20,...,90 percentiles")
lines(x, pcard(x, mu, rho), col = "orange")
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.