VGAM (version 1.0-4)

# Biamhcop: 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.

## Value

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

## 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.

`biamhcop`.

## Examples

Run this code
``````# NOT RUN {
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
# }
``````

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