bilogis {VGAM}

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.

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.

Value

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

Note

Gumbel (1961) proposed two bivariate logistic distributions with logistic distribution marginals, which he called Type I and Type II. The Type I is this one. The Type II belongs to the Morgenstern type. The biamhcop distribution has, as a special case, this distribution, which is when the random variables are independent.

Author(s)

T. W. Yee

References

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

See Also

bilogistic, biamhcop.

Examples

## 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") 
## End(Not run)