# bilogisUC: Bivariate Logistic Distribution

### Description

Density, distribution function, quantile function and random generation for the 4-parameter bivariate logistic distribution.

### Usage

 ```1 2 3``` ```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.

T. W. Yee

### References

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

`bilogistic`, `biamhcop`.

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```## 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) ```

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