R: Bivariate Logistic Distribution

bilogis {VGAM} | R Documentation

## 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 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 `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)

[Package VGAM version 1.1-3 Index]