hyperdirichlet (version 1.5-1)

diri_norm:

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

Run this code
diri_norm(runif(9))
gd_norm(1:3 , 3:1)

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