# dmixpois

0th

Percentile

##### Mixed Poisson Distribution

Density, distribution function, quantile function and random generation for a mixture of Poisson distributions.

Keywords
distribution
##### 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
x

vector of (non-negative integer) quantiles.

q

vector of quantiles.

p

vector of probabilities.

n

number of random values to return.

mu

Mean of the linear predictor. A single numeric value.

sd

Standard deviation of the linear predictor. A single numeric value.

invlink

Inverse link function. A function in the R language, used to transform the linear predictor into the parameter lambda of the Poisson distribution.

lower.tail

Logical. If TRUE (the default), probabilities are $P[X \le x]$, otherwise, $P[X > x]$.

GHorder

Number of quadrature points in the Gauss-Hermite quadrature approximation. A small positive integer.

##### Details

These functions are analogous to dpois ppois, qpois and rpois except that they apply to a mixture of Poisson distributions.

In effect, the Poisson mean parameter lambda is randomised by setting lambda = invlink(Z) where Z has a Gaussian $N(\mu,\sigma^2)$ distribution. The default is invlink=exp which means that lambda is lognormal. Set invlink=I to assume that lambda is approximately Normal.

For dmixpois, pmixpois and qmixpois, the probability distribution is approximated using Gauss-Hermite quadrature. For rmixpois, the deviates are simulated exactly.

##### Value

Numeric vector: dmixpois gives probability masses, ppois gives cumulative probabilities, qpois gives (non-negative integer) quantiles, and rpois generates (non-negative integer) random deviates.

##### See Also

dpois, gauss.hermite.

• dmixpois
• pmixpois
• qmixpois
• rmixpois
##### Examples
# NOT RUN {
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)
# }

Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)

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