dmultinomial function

The Vectorized Multinomial Distribution

Generate multinomially distributed random number vectors and compute multinomial probabilities.

dmultinomial(x, size=NULL, prob, log=FALSE)
rmultinomial(n, size, prob)

Examples

x <- c(100, 200, 700)
x1 <- matrix(c(100, 200, 700, 200, 100, 700, 700, 200, 100), byrow=TRUE, ncol=3)
p <- c(1, 2, 7)
p1 <- matrix(c(1, 2, 7, 2, 1, 7, 7, 2, 1), byrow=TRUE, ncol=3)
dmultinomial(x1, prob=p) 
## is equivalent to 
c(      dmultinom(x1[1, ], prob=p), 
        dmultinom(x1[2, ], prob=p), 
        dmultinom(x1[3, ], prob=p))

dmultinomial(x1, prob=p1, log=TRUE) 
## is equivalent to 
c(      dmultinom(x1[1, ], prob=p1[1, ], log=TRUE), 
        dmultinom(x1[2, ], prob=p1[2, ], log=TRUE), 
        dmultinom(x1[3, ], prob=p1[3, ], log=TRUE))

dmultinomial(x, prob=p1, log=TRUE)
## is equivalent to 
c(      dmultinom(x, prob=p1[1, ], log=TRUE), 
        dmultinom(x, prob=p1[2, ], log=TRUE), 
        dmultinom(x, prob=p1[3, ], log=TRUE))

prob <- c(1, 2, 7)
rmultinomial(4, 1000, prob)
rmultinomial(4, c(10, 100, 1000, 10000), prob)

## rmultinomial used with mcstoc
## (uncertain size and prob)
s <- mcstoc(rpois, "U", lambda=50)
p <- mcstoc(rdirichlet, "U", nvariates=3, alpha=c(4, 10, 20))
mcstoc(rmultinomial, "VU", nvariates=3, size=s, prob=p)

Arguments

• x: vector or matrix of length (or ncol) K of integers in 0:size .
• n: number of random vectors to draw.
• size: a vector of integers, say N, specifying the total number of objects that are put into K boxes in the typical multinomial experiment. For dmultinom , it defaults to sum(x) . The first element correspond to the vector prob or the first row of prob , ...
• prob: Numeric non-negative vector of length K, or matrix of size (x x K) specifying the probability for the K classes; is internally normalized to sum 1.
• log: Logical; if TRUE, log probabilities are computed.

Details

These functions are the vectorized versions of rmultinom and dmultinom. Recycling is permitted.