VGAM (version 0.7-1)

Card: Cardioid Distribution

Description

Density, distribution function, quantile function and random generation for the cardioid distribution.

Usage

dcard(x, mu, rho, log=FALSE)
pcard(q, mu, rho)
qcard(p, mu, rho, tolerance = 1e-07, maxits = 500)
rcard(n, mu, rho, ...)

Value

• dcard gives the density, pcard gives the distribution function, qcard gives the quantile function, and rcard generates random deviates.

Details

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.

See Also

cardioid.

Examples

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