Polono {VGAM}R Documentation

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.

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).

Value

dpolono gives the density, and rpolono generates random deviates.

Note

dpolono involves numerical integration that is performed using integrate. Consequently, computations may be very slow. Also, numerical problems may occur, and if so, then the use of ... may be needed.

For the maximum likelihood estimation of the 2 parameters a VGAM family function called polono, say, has not been written yet.

Author(s)

T. W. Yee

See Also

lognormal, poissonff, negbinomial.

Examples

## Not run: 
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)
## End(Not run)

[Package VGAM version 0.7-4 Index]