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]