Dirichlet-multinomial (multivariate Polya) distribution
Density function, cumulative distribution function and random generation for the Dirichlet-multinomial (multivariate Polya) distribution.
ddirmnom(x, size, alpha, log = FALSE) rdirmnom(n, size, alpha)
x |
k-column matrix of quantiles. |
size |
numeric vector; number of trials (zero or more). |
alpha |
k-values vector or k-column matrix; concentration parameter. Must be positive. |
log |
logical; if TRUE, probabilities p are given as log(p). |
n |
number of observations. If |
If (p[1],…,p[k]) ~ Dirichlet(α[1],…,α[k]) and (x[1],…,x[k]) ~ Multinomial(n, p[1],…,p[k]), then (x[1],…,x[k]) ~ DirichletMultinomial(n, α[1],…,α[k]).
Probability density function
f(x) = (n! * Γ(sum(α[k]))) / (Γ(n + sum(α[k]))) * prod((Γ(x[k] + α[k])) / (x[k]! * Γ(α[k]))
Gentle, J.E. (2006). Random number generation and Monte Carlo methods. Springer.
Kvam, P. and Day, D. (2001) The multivariate Polya distribution in combat modeling. Naval Research Logistics, 48, 1-17.
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.