Card {VGAM} | R Documentation

## 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, ...)

### Arguments

`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.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### 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.

### Value

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

### Note

Convergence problems might occur with `rcard`.

### Author(s)

Thomas W. Yee

### See Also

`cardioid`.

### Examples

    ## 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)

[Package VGAM version 0.7-9 Index]