Marginal density, distribution, survival and inverse survival functions for Liouville copulas or Liouville vectors.
The inverse survival function of Liouville vectors is not available in closed-form and is obtained numerically by root-finding.
As such, Monte-Carlo approximation have been considered for dealing with inference to avoid computational bottlenecks.
Note: the arguments of `sliouv`

are reversed since they are meant to be called inside `optim`

. The functions borrow
*psi* functions and their derivatives from the `copula-package`

.

1 2 3 4 5 6 7 |

`x` |
vector of quantiles from a Liouville copula (or a Liouville vector for the survival function , with support on the positive real line) |

`family` |
family of the Liouville copula. Either |

`alpha` |
integer Dirichlet parameter |

`theta` |
parameter of the corresponding Archimedean copula |

`u` |
vector of quantiles or survival probabilities, (pseudo)-uniform variates |

a vector with the corresponding quantile, probability, survival probabilities

1 2 3 4 5 6 7 8 9 10 | ```
#Marginal density
samp <- rliouv(n = 100, family = "clayton", alphavec <- c(2,3), theta = 2)
dliouvm(x=samp[,1], family="clayton", alpha=2, theta=2)
sum(log(dliouvm(x=samp[,1], family="clayton", alpha=2, theta=2)))
#Marginal distribution and (inverse) survival function
x <- rliouv(n = 100, family = "gumbel", alphavec <- c(2,3), theta = 2)
pliouvm(x[,1], family="gumbel", alpha=alphavec[1], theta=2)
su <- sliouvm(1-x[,1], family="gumbel", alpha=alphavec[1], theta=2)
isliouvm(u=su, family="clayton", alpha=2, theta=2)
#pliouv is the same as sliouv(isliouvm)
``` |

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