VGAM (version 1.1-8)

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)

Value

dbiamhcop gives the density,

pbiamhcop gives the distribution function, and

rbiamhcop generates random deviates (a two-column matrix).

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.

Author

T. W. Yee and C. S. Chee

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.

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)
if (FALSE) {
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
}