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}
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}
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\note{\code{dmultinom} is currently \emph{not vectorized} at all and has
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\note{\code{dmultinom} is currently \emph{not vectorized} at all and has
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  no C interface (API); this may be amended in the future.% yes, DO THIS!
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  no C interface (API); this may be amended in the future.% yes, DO THIS!
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}
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}
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\details{
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\details{
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  If \code{x} is a $K$-component vector, \code{dmultinom(x, prob)} is
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  If \code{x} is a \eqn{K}-component vector, \code{dmultinom(x, prob)}
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  the probability
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  is the probability
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  \deqn{P(X_1=x_1,\ldots,X_K=x_k) = C \times \prod_{j=1}^K
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  \deqn{P(X_1=x_1,\ldots,X_K=x_k) = C \times \prod_{j=1}^K
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    \pi_j^{x_j}}{P(X[1]=x[1], \dots , X[K]=x[k]) = C * prod(j=1 , \dots, K) p[j]^x[j]}
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    \pi_j^{x_j}}{P(X[1]=x[1], \dots , X[K]=x[k]) = C * prod(j=1 , \dots, K) p[j]^x[j]}
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  where \eqn{C} is the \sQuote{multinomial coefficient}
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  where \eqn{C} is the \sQuote{multinomial coefficient}
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  \eqn{C = N! / (x_1! \cdots x_K!)}{C = N! / (x[1]! * \dots * x[K]!)}
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  \eqn{C = N! / (x_1! \cdots x_K!)}{C = N! / (x[1]! * \dots * x[K]!)}
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  and \eqn{N = \sum_{j=1}^K x_j}{N = sum(j=1, \dots, K) x[j]}.
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  and \eqn{N = \sum_{j=1}^K x_j}{N = sum(j=1, \dots, K) x[j]}.
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  and
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  and
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  \eqn{P_j = \pi_j / (1 - \sum_{k=1}^{j-1} \pi_k)}{P[j] = p[j] / (1 - sum(p[1:(j-1)]))}.
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  \eqn{P_j = \pi_j / (1 - \sum_{k=1}^{j-1} \pi_k)}{P[j] = p[j] / (1 - sum(p[1:(j-1)]))}.
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}
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}
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\value{
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\value{
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  For \code{rmultinom()},
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  For \code{rmultinom()},
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  an integer \code{K x n} matrix where each column is a random vector
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  an integer \eqn{K \times n}{K x n} matrix where each column is a
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  generated according to the desired multinomial law, and hence summing
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  random vector generated according to the desired multinomial law, and
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  to \code{size}.  Whereas the \emph{transposed} result would seem more
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  hence summing to \code{size}.  Whereas the \emph{transposed} result
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  natural at first, the returned matrix is more efficient because of
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  would seem more natural at first, the returned matrix is more
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  columnwise storage.
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  efficient because of columnwise storage.
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}
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}
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\seealso{
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\seealso{
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  \link{Distributions} for standard distributions, including
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  \link{Distributions} for standard distributions, including
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  \code{\link{dbinom}} which is a special case conceptually.
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  \code{\link{dbinom}} which is a special case conceptually.
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%% but does not return 2-vectors
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%% but does not return 2-vectors