Bivariate Logistic Distribution
Density, distribution function, quantile function and random generation for the 4-parameter bivariate logistic distribution.
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)
x1, x2, q1, q2 |
vector of quantiles. |
n |
number of observations.
Same as |
loc1, loc2 |
the location parameters l1 and l2. |
scale1, scale2 |
the scale parameters s1 and s2. |
log |
Logical.
If |
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.
dbilogis gives the density,
pbilogis gives the distribution function, and
rbilogis generates random deviates (a two-column matrix).
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
Gumbel, E. J. (1961). Bivariate logistic distributions. Journal of the American Statistical Association, 56, 335–349.
## 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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