R: Ali-Mikhail-Haq Bivariate Distribution

Biamhcop {VGAM} | R Documentation

## Ali-Mikhail-Haq Bivariate Distribution

### Description

Density, distribution function, and random generation for the (one parameter) bivariate Ali-Mikhail-Haq distribution.

### Usage

    dbiamhcop(x1, x2, apar, log = FALSE)
    pbiamhcop(q1, q2, apar)
    rbiamhcop(n, apar)

### Arguments

`x1, x2, q1, q2` | vector of quantiles.
`n` | number of observations. Same as `runif`
`apar` | the association parameter.
`log` | Logical. If `TRUE` then the logarithm is returned.

### Details

See `biamhcop`, the VGAM family functions for estimating the parameter by maximum likelihood estimation, for the formula of the cumulative distribution function and other details.

### Value

`dbiamhcop` gives the density, `pbiamhcop` gives the distribution function, and `rbiamhcop` generates random deviates (a two-column matrix).

### Author(s)

T. W. Yee and C. S. Chee

### See Also

`biamhcop`.

### Examples

     x <- seq(0, 1, len = (N <- 101)); apar <- 0.7
    ox <- expand.grid(x, x)
    zedd <- dbiamhcop(ox[, 1], ox[, 2], apar = apar)
    ## Not run:
    contour(x, x, matrix(zedd, N, N), col = "blue")
    zedd <- pbiamhcop(ox[, 1], ox[, 2], apar = apar)
    contour(x, x, matrix(zedd, N, N), col = "blue")

    plot(r <- rbiamhcop(n = 1000, apar = apar), col = "blue")
    par(mfrow = c(1, 2))
    hist(r[, 1])  # Should be uniform
    hist(r[, 2])  # Should be uniform

    ## End(Not run)

[Package VGAM version 1.0-3 Index]