# BiCopCDF: Distribution function of a bivariate copula In CDVine: Statistical Inference of C- And D-Vine Copulas

## Description

This function evaluates the cumulative distribution function (CDF) of a given parametric bivariate copula.

## Usage

 `1` ```BiCopCDF(u1, u2, family, par, par2=0) ```

## Arguments

 `u1,u2` Numeric vectors of equal length with values in [0,1]. `family` An integer defining the bivariate copula family: `0` = independence copula `1` = Gaussian copula `2` = Student t copula (t-copula) `3` = Clayton copula `4` = Gumbel copula `5` = Frank copula `6` = Joe copula `7` = BB1 copula `8` = BB6 copula `9` = BB7 copula `10` = BB8 copula `13` = rotated Clayton copula (180 degrees; “survival Clayton”) `14` = rotated Gumbel copula (180 degrees; “survival Gumbel”) `16` = rotated Joe copula (180 degrees; “survival Joe”) `17` = rotated BB1 copula (180 degrees; “survival BB1”) `18` = rotated BB6 copula (180 degrees; “survival BB6”) `19` = rotated BB7 copula (180 degrees; “survival BB7”) `20` = rotated BB8 copula (180 degrees; “survival BB8”) `23` = rotated Clayton copula (90 degrees) `24` = rotated Gumbel copula (90 degrees) `26` = rotated Joe copula (90 degrees) `27` = rotated BB1 copula (90 degrees) `28` = rotated BB6 copula (90 degrees) `29` = rotated BB7 copula (90 degrees) `30` = rotated BB8 copula (90 degrees) `33` = rotated Clayton copula (270 degrees) `34` = rotated Gumbel copula (270 degrees) `36` = rotated Joe copula (270 degrees) `37` = rotated BB1 copula (270 degrees) `38` = rotated BB6 copula (270 degrees) `39` = rotated BB7 copula (270 degrees) `40` = rotated BB8 copula (270 degrees) `par` Copula parameter. `par2` Second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8; default: `par2 = 0`).

## Value

A numeric vector of the bivariate copula distribution function evaluated at `u1` and `u2`.

## Author(s)

Eike Brechmann

`BiCopPDF`, `BiCopHfunc`, `BiCopSim`
 ```1 2 3 4 5 6 7``` ```# simulate from a bivariate t-copula simdata = BiCopSim(300,2,-0.7,par2=4) # evaluate the distribution function of the bivariate t-copula u1 = simdata[,1] u2 = simdata[,2] BiCopCDF(u1,u2,2,-0.7,par2=4) ```