Description Usage Arguments Details Note Author(s) References See Also Examples
View source: R/density_joint.R
Density of a Gamma distributed variable X and a (zero-truncated) Poisson variable Y if their joint distribution is defined via a copula
1 | density_joint(x, y, mu, delta, lambda, theta, family,zt)
|
x |
vector at which the density is evaluated |
y |
vector at which the density is evaluated |
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 |
zt |
logical. If |
For a Gamma distributed variable X and a (zero truncated) Possion variable Y, their joint density function is given by
f_{XY}(x,y)=f_X(x) ≤ft(D_u(F_Y(y),F_X(x)|θ) - D_u(F_Y(y-1),F_X(x)|θ) \right)\,.
Here D_u is the h-function of a copula famila family
with copula parameter theta
.
We allow two options: If mu and lambda are vectors of the same length as x and y, we evaluate the density for the corresponding parameter values. Otherwise, lambda and nu have to be numbers, and the parameters are the same for all entries of x and y.
Nicole Kraemer
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.
1 | out<-density_joint(2,3,mu=1,delta=1,lambda=4,theta=0.5,family=1)
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.