# simulate_joint

##### Simulation from the joint model

Simulation from the joint model

- Keywords
- datagen

##### Usage

`simulate_joint(n, mu, delta, lambda, theta, family, max.y = 5000, eps = 1e-05,zt=TRUE)`

##### Arguments

- n
- number of samples
- mu
- expectation of the Gamma distribution
- delta
- dispersion parameter of the Gamma distribution
- lambda
- parameter of the (zero-truncated) Poisson distribution
- theta
- copula parameter
- family
- an integer defining the bivariate copula family: 1 = Gauss, 3 = Clayton, 4=Gumbel, 5=Frank
- max.y
- upper value for the conditional (zero truncated) Poisson variable, see below for more details
- eps
- precision, see below for more details
- zt
- logical. If
`zt=TRUE`

, we use a zero-truncated Poisson variable. Otherwise, we use a Poisson variable. Default is`TRUE`

.

##### Details

For a Gamma distributed variable X and a (zero truncated) Possion variable Y, we sample from their joint distribution that is given by the density function
$$f_{XY}(x,y)=f_X(x) \left(D_u(F_Y(y),F_X(x)|\theta) - D_u(F_Y(y-1),F_X(x)|\theta) \right)\,.$$Here $D_u$ is the h-function of a copula famila `family`

with copula parameter `theta`

. First, we sample n observations `x`

from the marginal Gamma distribution. Second, for each x, we then sample an observation from the conditional distribution of Y given X=x. In the second step, the conditional distribution is evaluated up to the maximum of `max.y`

and the smallest integer > `y.max`

for which the conditional probability is smaller than `eps`

.

##### Value

- n samples, stored in a $n \times 2$ matrix

##### References

N. Kraemer, E. Brechmann, D. Silvestrini, C. Czado (2013): Total loss estimation using copula-based regression models. Insurance: Mathematics and Economics 53 (3), 829 - 839.

##### See Also

##### Examples

```
library(VineCopula)
n<-100 # number of observations
mu<-1000
delta<-0.09
lambda<-2.5
family<-1
theta<-BiCopTau2Par(tau=0.5,family=family)
my.data<-simulate_joint(n,mu,delta,lambda,theta,family)
```

*Documentation reproduced from package CopulaRegression, version 0.1-5, License: GPL (>= 2.0)*