VGAM (version 1.0-4)

# 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)

## 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.

## Value

dbilogis gives the density, pbilogis gives the distribution function, and rbilogis generates random deviates (a two-column matrix).

## 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.

## Examples

Run this code
# NOT RUN {
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")
# }

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