VGAM (version 0.7-3)

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)

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)