Kendall.SNBP {Bivariate.Pareto}

Kendall's tau under the SNBP distribution

Description

Compute Kendall's tau under the Sankaran and Nair bivairate Pareto (SNBP) distribution (Sankaran and Nair, 1993) by numerical integration.

Usage

Kendall.SNBP(Alpha0, Alpha1, Alpha2, Gamma)

Arguments

Alpha0

Copula parameter \alpha_{0} with restricted range.

Alpha1

Positive scale parameter \alpha_{1} for the Pareto margin.

Alpha2

Positive scale parameter \alpha_{2} for the Pareto margin.

Gamma

Common positive shape parameter \gamma for the Pareto margins.

Details

The admissible range of Alpha0 (\alpha_{0}) is 0 \leq \alpha_{0} \leq (\gamma+1) \alpha_{1} \alpha_{2}.

Value

tau

Kendall's tau.

References

Sankaran PG, Nair NU (1993), A bivariate Pareto model and its applications to reliability, Naval Research Logistics, 40:1013-1020.

Shih J-H, Lee W, Sun L-H, Emura T (2019), Fitting competing risks data to bivariate Pareto models, Communications in Statistics - Theory and Methods, 48:1193-1220.

Examples

library(Bivariate.Pareto)
Kendall.SNBP(7e-5,0.0036,0.0075,1.8277)