Plackett's Bivariate Copula
Density, distribution function, and random generation for the (one parameter) bivariate Plackett copula.
dbiplackcop(x1, x2, oratio, log = FALSE) pbiplackcop(q1, q2, oratio) rbiplackcop(n, oratio)
x1, x2, q1, q2 |
vector of quantiles. |
n |
number of observations.
Same as in |
oratio |
the positive odds ratio psi. |
log |
Logical.
If |
See biplackettcop, the VGAM
family functions for estimating the
parameter by maximum likelihood estimation, for the formula of the
cumulative distribution function and other details.
dbiplackcop gives the density,
pbiplackcop gives the distribution function, and
rbiplackcop generates random deviates (a two-column matrix).
T. W. Yee
Mardia, K. V. (1967). Some contributions to contingency-type distributions. Biometrika, 54, 235–249.
## Not run: N <- 101; oratio <- exp(1) x <- seq(0.0, 1.0, len = N) ox <- expand.grid(x, x) zedd <- dbiplackcop(ox[, 1], ox[, 2], oratio = oratio) contour(x, x, matrix(zedd, N, N), col = "blue") zedd <- pbiplackcop(ox[, 1], ox[, 2], oratio = oratio) contour(x, x, matrix(zedd, N, N), col = "blue") plot(rr <- rbiplackcop(n = 3000, oratio = oratio)) par(mfrow = c(1, 2)) hist(rr[, 1]) # Should be uniform hist(rr[, 2]) # Should be uniform ## End(Not run)
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