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 if true then the prior, likelihood, posterior as well as the posterior values of r and v are returned as a list.

Value

If ret is true, then 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)
retval<-poisgamp(y,6,3,ret=TRUE)
c.i.<-qgamma(c(0.025,0.975),retval$r, retval$v)
cat(paste("95% credible interval for mu: [",round(c.i.[1],3), ",", round(c.i.[2],3)),"]\n") 


[Package Bolstad version 0.2-14 Index]