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, 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 l1 and l2.
`scale1, scale2` | the scale parameters s1 and s2.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### 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 0.7-9 Index]