DirMnom {extraDistr} | R Documentation |
Dirichlet-multinomial (multivariate Polya) distribution
Description
Density function, cumulative distribution function and random generation
for the Dirichlet-multinomial (multivariate Polya) distribution.
Usage
ddirmnom(x, size, alpha, log = FALSE)
rdirmnom(n, size, alpha)
Arguments
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 length(n) > 1 ,
the length is taken to be the number required.
|
Details
If (p1,…,pk)∼Dirichlet(α1,…,αk)
and
(x1,…,xk)∼Multinomial(n,p1,…,pk)
, then
(x1,…,xk)∼DirichletMultinomial(n,α1,…,αk)
.
Probability density function
f(x)=Γ(n+∑αk)(n!)Γ(∑αk)∏k=1K(xk!)Γ(αk)Γ(xk+αk)
References
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.
See Also
Dirichlet
, Multinomial
[Package
extraDistr version 1.10.0
Index]