VGAM (version 0.7-5)

Polono: The Poisson Lognormal Distribution

Description

Density, and random generation for the Poisson lognormal distribution.

Usage

dpolono(x, meanlog=0, sdlog=1, ...)
rpolono(n, meanlog=0, sdlog=1)

Arguments

x

vector of quantiles.

n

number of observations. Must be a positive integer of length 1.

meanlog, sdlog

the mean and standard deviation of the normal distribution (on the log scale). They match the arguments in Lognormal.

...

Arguments passed into integrate.

Value

• dpolono gives the density, and rpolono generates random deviates.

Details

The Poisson lognormal distribution is similar to the negative binomial in that it can be motivated by a Poisson distribution whose mean parameter comes from a right skewed distribution (gamma for the negative binomial and lognormal for the Poisson lognormal distribution).

See Also

lognormal, poissonff, negbinomial.

Examples

meanlog = 0.5; sdlog = 0.5
y = 0:19
proby = dpolono(y, m=meanlog, sd=sdlog)
plot(y, proby, type="h", col="blue", las=1, ylab="P[Y=y]", log="",
     main=paste("Poisson lognormal(meanlog=",meanlog,", sdlog=",sdlog,")",
                sep=""))
sum(proby)  # Should be 1

y = rpolono(n=1000, m=meanlog, sd=sdlog)
table(y)
hist(y, breaks=((-1):max(y))+0.5, prob=TRUE)