VGAM (version 1.1-12)

bilogis: Bivariate Logistic Distribution

Description

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

Usage

dbilogis(x1, x2, loc1 = 0, scale1 = 1, loc2 = 0, scale2 = 1,
         log = FALSE)
pbilogis(q1, q2, loc1 = 0, scale1 = 1, loc2 = 0, scale2 = 1)
rbilogis(n, loc1 = 0, scale1 = 1, loc2 = 0, scale2 = 1)

Value

dbilogis gives the density,

pbilogis gives the distribution function, and

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

Arguments

x1, x2, q1, q2

vector of quantiles.

n

number of observations. Same as rlogis.

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.

Author

T. W. Yee

Details

See bilogis, 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

bilogistic, biamhcop.

Examples

if (FALSE)  par(mfrow = c(1, 3))
ymat <- rbilogis(n = 2000, 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 <- dbilogis(ox[,1], ox[,2], loc1 = 5, loc2 = 7, scale2 = exp(1))
contour(x1, x2, matrix(z, N, N), main = "density")
z <- pbilogis(ox[,1], ox[,2], loc1 = 5, loc2 = 7, scale2 = exp(1))
contour(x1, x2, matrix(z, N, N), main = "cdf")