VGAM (version 0.8-5)

bilogis4: Bivariate Logistic Distribution

Description

Density, distribution function, quantile function and random generation for the 4-parameter bivariate logistic distribution.

Usage

dbilogis4(x1, x2, loc1 = 0, scale1 = 1, loc2 = 0, scale2 = 1, log = FALSE)
pbilogis4(q1, q2, loc1 = 0, scale1 = 1, loc2 = 0, scale2 = 1)
rbilogis4(n, loc1 = 0, scale1 = 1, loc2 = 0, scale2 = 1)

Arguments

x1, x2, q1, q2

vector of quantiles.

n

number of observations. Must be a positive integer of length 1.

loc1, loc2

the location parameters $l_1$ and $l_2$.

scale1, scale2

the scale parameters $s_1$ and $s_2$.

log

Logical. If log = TRUE then the logarithm of the density is returned.

Value

• dbilogis4 gives the density, pbilogis4 gives the distribution function, and rbilogis4 generates random deviates (a two-column matrix).

Details

See bilogis4, the VGAM family function for estimating the four parameters by maximum likelihood estimation, for the formula of the cumulative distribution function and other details.

References

Gumbel, E. J. (1961) Bivariate logistic distributions. Journal of the American Statistical Association, 56, 335--349.

See Also

bilogistic4.

Examples

par(mfrow = c(1, 3))
n = 2000
ymat = rbilogis4(n, loc1 = 5, loc2 = 7, scale2 = exp(1))
myxlim = c(-2, 15)
myylim = c(-10, 30)
plot(ymat, xlim = myxlim, ylim = myylim)

N = 100
x1 = seq(myxlim[1], myxlim[2], len = N)
x2 = seq(myylim[1], myylim[2], len = N)
ox = expand.grid(x1, x2)
z = dbilogis4(ox[,1], ox[,2], loc1 = 5, loc2 = 7, scale2 = exp(1))
contour(x1, x2, matrix(z, N, N), main = "density")
z = pbilogis4(ox[,1], ox[,2], loc1 = 5, loc2 = 7, scale2 = exp(1))
contour(x1, x2, matrix(z, N, N), main = "cdf")