copula2d: Some Bivariate Copulas

In mable: Maximum Approximate Bernstein/Beta Likelihood Estimation

Some Bivariate Copulas

Description

Parametric bivariate copulas, densities, and random number generators

Usage

d2dcop.asym(u, v, lambda, copula = "clayton", ...)

p2dcop.asym(u, v, lambda, copula = "clayton", ...)

r2dcop.asym(n, lambda, copula = "clayton", ...)

dcopula(u, v, copula, ...)

pcopula(u, v, copula, ...)

rcopula(n, copula, ...)

Arguments

u, v	vectors of same length at which the copula and its density is evaluated
lambda	a vector of three mixing proportions which sum to one
copula	the name of a copula to be called or a base copula for construncting asymmetric copula(see Details)
...	the parameter(s) of copula, theta for most of the models, and df, the degrees of freedom if copula='t', or m if copula='nakagami'
n	number of random vectors to be generated

Details

The names of available copulas are 'amh' (Ali-Mikhai-Haq), 'bern' (Bernstein polynomial model), 'clayton'(Clayton), 'exponential' (Exponential), 'fgm'(Farlie–Gumbel–Morgenstern), 'frank' (Frank), 'gauss' (Gaussian), 'gumbel' (Gumbel), 'indep' (Independence), 'joe' (Joe), 'nakagami' (Nakagami-m), 'plackett' (Plackett), 't' (Student's t). d2dcop.asym, etc, calculate the constructive assymmetric copula of Wu (2014) using base copula C_{\theta} with mixing proportions p=(\lambda_1,\lambda_2,\lambda_3) and parameter values \theta=(\theta_1,\theta_2,\theta_3): \lambda_0C_{\theta_0}(u,v)+\lambda_1[v-C_{\theta_1}(1-u,v)]+\lambda_2[u-C_{\theta_2}(u,1-v)]. If copula='t' or 'nakagami', df or m must be also given.

Value

a vector of copula ot its density values evaluated at (u,v) or an n x 2 matrix of the generated observations

References

Nelsen, R. B. (1999). An Introduction to Copulas. Springer Series in Statistics. New York: Springer. Wu, S. (2014). Construction of asymmetric copulas and its application in two-dimensional reliability modelling. European Journal of Operational Research 238 (2), 476–485.

mable documentation built on Oct. 1, 2024, 9:06 a.m.