bilogisUC: Bivariate Logistic Distribution In VGAM: Vector Generalized Linear and Additive Models

 bilogis 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 `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.

T. W. Yee

References

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

`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)
``````

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.