bilogis4 {VGAM}R Documentation

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)
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 l1 and l2.
scale1, scale2 the scale parameters s1 and s2.

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.

Value

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

Author(s)

T. W. Yee

References

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

See Also

bilogistic4.

Examples

## Not run: 
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")
## End(Not run)

[Package VGAM version 0.7-7 Index]