VGAM (version 0.9-3)

Amh: Ali-Mikhail-Haq 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. Same as runif

alpha

the association parameter.

log

Logical. If TRUE then the logarithm is returned.

Value

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

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.

See Also

amh.

Examples

x <- seq(0, 1, len = (N <- 101)); alpha <- 0.7
ox <- expand.grid(x, x)
zedd <- damh(ox[, 1], ox[, 2], alpha = alpha)
contour(x, x, matrix(zedd, N, N), col = "blue")
zedd <- pamh(ox[, 1], ox[, 2], alpha = alpha)
contour(x, x, matrix(zedd, 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