copula_psi: Copula multiplier and diagonal functions of exchangeable...

In qdfauction: Nonparametric Quantile Density Estimation and Structural Analysis of First-Price Auctions

Copula multiplier and diagonal functions of exchangeable Archimedean copulas

Description

For an exchangeable n-dimensional Archimedean copula C: * 'copula_psi()' is the copula multiplier of Doosti (2026a), \psi(u) = C_2(u,\ldots,u)/c(u,\ldots,u), which enters the inverse bid function v = b + \psi(u)\,q(u). Under independence \psi(u) = u/(n-1) and the GPV formula is recovered. * 'copula_delta()' is the diagonal \delta(u) = C(u,\ldots,u), the distribution function of the maximum of the n uniform scores. * 'copula_delta_prime()' is its derivative.

Usage

copula_psi(u, family = "independence", theta = NULL, n)

copula_delta(u, family = "independence", theta = NULL, n)

copula_delta_prime(u, family = "independence", theta = NULL, n)

Arguments

u	numeric vector in (0, 1).
family	'"independence"', '"clayton"', '"gumbel"' or '"frank"'.
theta	copula parameter (ignored for independence).
n	number of bidders.

Value

numeric vector.

References

Doosti, H. (2026a). A copula-quantile density approach to affiliated private value auctions. *Economics Letters*, 261, 112837. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.econlet.2026.112837")}

Examples

u <- c(0.2, 0.5, 0.8)
copula_psi(u, "clayton", theta = 2, n = 3)
copula_psi(u, "independence", n = 3)      # u / (n - 1)
copula_delta(u, "gumbel", theta = 1.5, n = 3)

qdfauction documentation built on Nov. 10, 2026, 5:07 p.m.