VGAM (version 1.0-4)

# biclaytoncop: Clayton Copula (Bivariate) Family Function

## Description

Estimate the correlation parameter of the (bivariate) Clayton copula distribution by maximum likelihood estimation.

## Usage

biclaytoncop(lapar = "loge", iapar = NULL, imethod = 1,
parallel = FALSE, zero = NULL)

## Arguments

lapar, iapar, imethod

Details at CommonVGAMffArguments. See Links for more link function choices.

parallel, zero

Details at CommonVGAMffArguments. If parallel = TRUE then the constraint is also applied to the intercept.

## Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

## Details

The cumulative distribution function is $$P(u_1, u_2;\alpha) = (u_1^{-\alpha} + u_2^{-\alpha}-1)^{-1/\alpha}$$ for $$0 \leq \alpha$$. Here, $$\alpha$$ is the association parameter. The support of the function is the interior of the unit square; however, values of 0 and/or 1 are not allowed (currently). The marginal distributions are the standard uniform distributions. When $$\alpha = 0$$ the random variables are independent.

This VGAM family function can handle multiple responses, for example, a six-column matrix where the first 2 columns is the first out of three responses, the next 2 columns being the next response, etc.

## References

Clayton, D. (1982) A model for association in bivariate survival data. Journal of the Royal Statistical Society, Series B, Methodological, 44, 414--422.

Stober, J. and Schepsmeier, U. (2013) Derivatives and Fisher information of bivariate copulas. Statistical Papers.

rbiclaytoncop, dbiclaytoncop, kendall.tau.

## Examples

Run this code
# NOT RUN {
ymat <- rbiclaytoncop(n = (nn <- 1000), apar = exp(2))
bdata <- data.frame(y1 = ymat[, 1],
y2 = ymat[, 2],
y3 = ymat[, 1],
y4 = ymat[, 2],
x2 = runif(nn))

summary(bdata)
# }
# NOT RUN {
plot(ymat, col = "blue")
# }
# NOT RUN {
fit1 <- vglm(cbind(y1, y2, y3, y4) ~ 1,  # 2 responses, e.g., (y1,y2) is the first
biclaytoncop, data = bdata,
trace = TRUE, crit = "coef")  # Sometimes a good idea

coef(fit1, matrix = TRUE)
Coef(fit1)
summary(fit1)

# Another example; apar is a function of x2
bdata <- transform(bdata, apar = exp(-0.5 + x2))
ymat <- rbiclaytoncop(n = nn, apar = with(bdata, apar))
bdata <- transform(bdata, y5 = ymat[, 1],
y6 = ymat[, 2])
fit2 <- vgam(cbind(y5, y6) ~ s(x2), data = bdata,
biclaytoncop(lapar = "loge"), trace = TRUE)
# }
# NOT RUN {
plot(fit2, lcol = "blue", scol = "orange", se = TRUE, las = 1)
# }


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