hyperdirichlet (version 1.4-2)

diri_norm: Normalization constants for the Dirichlet and generalized Dirichlet distributions

Description

Normalization constants for the Dirichlet and generalized Dirichlet distributions using computationally efficient methods

Usage

diri_norm(x)
gd_norm(a,b)

Arguments

x

Vector of parameters in the Dirichlet distribution

a,b

Vectors of parameters in the generalized Dirichlet distribution

Value

• Returns the normalization constant:

  $$\frac{ \prod_{i=1}^{k}\Gamma\left(\alpha_i\right) }{ \Gamma\left(\sum_{i=1}^{k}\alpha_i\right) }$$

  for the Dirichlet and

  $$\frac{\prod_{i=1}^{k}\Gamma\left(a_i\right)\Gamma\left(b_i\right) }{ \prod_{i=1}^{k}\Gamma\left(a_i+b_i\right) }$$ for the generalized Dirichlet.

References

R. J. Connor and J. E. Mosimann 1969. Concepts of independence for proportions with a generalization of the Dirichlet distribution. Journal of the American Statistical Association, volume 64, number 325, pp194-206

See Also

dhyperdirichlet

Examples

diri_norm(runif(9))
gd_norm(1:3 , 3:1)