dmixpois.Rd
\name{dmixpois}
\alias{dmixpois}
\alias{pmixpois}
\alias{qmixpois}
\alias{rmixpois}
\title{
Mixed Poisson Distribution
}
\description{
Density, distribution function, quantile function and random
generation for a mixture of Poisson distributions.
}
\usage{
dmixpois(x, mu, sd, invlink = exp, GHorder = 5)
pmixpois(q, mu, sd, invlink = exp, lower.tail = TRUE, GHorder = 5)
qmixpois(p, mu, sd, invlink = exp, lower.tail = TRUE, GHorder = 5)
rmixpois(n, mu, sd, invlink = exp)
}
\arguments{
\item{x}{vector of (non-negative integer) quantiles.}
\item{q}{vector of quantiles.}
\item{p}{vector of probabilities.}
\item{n}{number of random values to return.}
\item{mu}{
Mean of the linear predictor. A single numeric value.
}
\item{sd}{
Standard deviation of the linear predictor. A single numeric value.
}
\item{invlink}{
Inverse link function. A function in the \R language,
used to transform the linear predictor into the
parameter \code{lambda} of the Poisson distribution.
}
\item{lower.tail}{
Logical. If \code{TRUE} (the default), probabilities are
\eqn{P[X \le x]}, otherwise, \eqn{P[X > x]}.
}
\item{GHorder}{
Number of quadrature points in the Gauss-Hermite quadrature approximation.
A small positive integer.
}
}
\details{
These functions are analogous to
\code{\link{dpois}}
\code{\link{ppois}},
\code{\link{qpois}} and
\code{\link{rpois}}
except that they apply to a mixture of Poisson distributions.
In effect, the Poisson mean parameter \code{lambda} is randomised
by setting \code{lambda = invlink(Z)} where \code{Z}
has a Gaussian \eqn{N(\mu,\sigma^2)}{N(\mu, \sigma^2)} distribution.
The default is \code{invlink=exp} which means that
\code{lambda} is lognormal. Set \code{invlink=I} to assume
that \code{lambda} is approximately Normal.
For \code{dmixpois}, \code{pmixpois} and \code{qmixpois},
the probability distribution is approximated using Gauss-Hermite
quadrature. For \code{rmixpois}, the deviates are simulated
exactly.
}
\value{
Numeric vector:
\code{dmixpois} gives probability masses,
\code{ppois} gives cumulative probabilities,
\code{qpois} gives (non-negative integer) quantiles, and
\code{rpois} generates (non-negative integer) random deviates.
}
\seealso{
\code{\link{dpois}},
\code{\link{gauss.hermite}}.
}
\examples{
dmixpois(7, 10, 1, invlink = I)
dpois(7, 10)
pmixpois(7, log(10), 0.2)
ppois(7, 10)
qmixpois(0.95, log(10), 0.2)
qpois(0.95, 10)
x <- rmixpois(100, log(10), log(1.2))
mean(x)
var(x)
}
\author{\adrian
,
\rolf
and \ege
}
\keyword{distribution}