poisgamp {Bolstad} | R Documentation |
Evaluates and plots the posterior density for mu, the mean rate of occurance in a Poisson process and a gamma prior on mu
poisgamp(y, r, v, ret = FALSE)
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 |
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 |
## 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")