Amh {VGAM} | R Documentation

## Ali-Mikhail-Haq Distribution's Bivariate Distribution

### Description

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

### Usage

    damh(x1, x2, alpha, log=FALSE)
    pamh(q1, q2, alpha)
    ramh(n, alpha)

### Arguments

`x1, x2, q1, q2` | vector of quantiles.
`n` | number of observations. Must be a positive integer of length 1.
`alpha` | the association parameter.
`log` | Logical. If `TRUE` then the logarithm is returned.

### Details

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

### Value

`damh` gives the density, `pamh` gives the distribution function, and `ramh` generates random deviates (a two-column matrix).

### Author(s)

T. W. Yee and C. S. Chee

### See Also

`amh`.

### Examples

    x = seq(0, 1, len=(N <- 101))
    alpha = 0.7
    ox = expand.grid(x, x)
    z = damh(ox[,1], ox[,2], alpha=alpha)
    ## Not run:
    contour(x, x, matrix(z, N, N), col="blue")
    z = pamh(ox[,1], ox[,2], alpha=alpha)
    contour(x, x, matrix(z, N, N), col="blue")

    plot(r <- ramh(n=1000, alpha=alpha), 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 0.7-9 Index]