dclayton: calculate the density of Clayton copula.

In MonkeyLB/TDR: Estimate the reproducibility of sequencing-based experiment

Description

compute the density of Clayton copula given the two individual variables.

Usage

dclayton(u, v, beta)

Arguments

u	a vector containing cumulative densities for one replicate data.
v	a vector containing cumulative densities for the other replicate data.
beta	the single paramter for the Clayton copula. It has a range of (0, ∞), perfect dependence is archieved if β approximates ∞, while β approximates 0 implies no dependence.

Details

The formula for the density of bivariate Clayton copula is:

c(u, v | β) = (1+β)*((u*v)^(-1-β))*(u^(-β)+v^(-β)-1)^(-1/β-2)

where β > 0 in our application.

Value

dclayton calculates the density of Clayton copula given the cumulative densities of two random variables and the parameter of Clayton copula. The empirical cumulative densities of the two random variables could be obtained using the function empdist(). Invalid arguments will result in value NaN.

References

Nelsen, R. (2006). An Introduction to Copula, Second Edition, Springer. G. G. Venter (2001). Tails of copulas. In Proceedings ASTIN Washington, USA, pages 68-113.

Examples

data(Chipseq_TF)
x1 <- Chipseq_TF[,1]
x2 <- Chipseq_TF[,2]
U=empdist(x1, x2)
u <- U[,1]
v <- U[,2]
beta <- 2
dclayton(u, v, beta)

MonkeyLB/TDR documentation built on May 7, 2019, 4:59 p.m.