poisgamp {Bolstad}R Documentation

Poisson sampling with a gamma prior

Description

Evaluates and plots the posterior density for mu, the mean rate of occurance in a Poisson process and a gamma prior on mu

Usage

poisgamp(y, r, v, ret = FALSE)

Arguments

y a random sample from a Poisson distribution.
r the shape parameter of the gamma prior.
v the rate parameter of the gamma prior. Note that the scale is 1/v
ret This argument is deprecated and has no effect

Value

A list will be returned with the following components:

prior the prior density assigned to mu
likelihood the scaled likelihood function for mu given y
posterior the posterior probability of mu given y
r the shape parameter for the gamma posterior
v the rate parameter for the gamma posterior

See Also

poisdp poisgcp

Examples

## simplest call with an observation of 4 and a gamma(1,1), i.e. an exponential prior on the
## mu
poisgamp(4,1,1)

##  Same as the previous example but a gamma(10,1) prior
poisgamp(4,10,1)

##  Same as the previous example but an improper gamma(1,0) prior
poisgamp(4,1,0)

## A random sample of 50 observations from a Poisson distribution with
## parameter mu = 3 and  gamma(6,3) prior
y = rpois(50,3)
poisgamp(y,6,3)

## In this example we have a random sample from a Poisson distribution
## with an unknown mean. We will use a gamma(6,3) prior to obtain the
## posterior gamma distribution, and use the R function qgamma to get a
## 95% credible interval for mu
y = c(3,4,4,3,3,4,2,3,1,7)
results = poisgamp(y,6,3)
ci = qgamma(c(0.025,0.975),results$r, results$v)
cat(paste("95% credible interval for mu: [",round(ci[1],3), ",", round(ci[2],3)),"]\n")


[Package Bolstad version 0.2-17 Index]