poisgamma: Poisson sampling distribution with a gamma distribution of...

In yijin71/statg012: statg012: Statistical Inference at UCL

Description

Define the posterior distribution function for π ( μ | x ), with a gamma prior distribution π ( μ; α, λ ) and a poisson sampling distribution f (x | μ).

Usage

poisgamma(x, shape, rate, scale = 1/rate)

Arguments

x	the sample data from poisson distribution (x > 0).
shape	the shape parameter for a gamma distribution (> 0).
rate	the rate parameter for a gamma distribution (> 0).
scale	equals 1 / rate (> 0).

Value

An object of class "g12post" is returned.

prior	the prior distribution, i.e. the gamma(α,λ) distribution.
likelihood	the likelihood function of x given μ, i.e. the Poisson( x | μ) distribution.
posterior	the posterior distribution of μ given x.
mu	the expected number of occurence which is the parameter of poisson distribution.
pri.shape	the shape parameter for the gamma distribution of prior.
pri.rate	the rate parameter for the gamma distribution of prior.
pos.shape	the shape parameter for the gamma distribution of posterior.
pos.rate	the rate parameter for the gamma distribution of posterior.
model	the prior and likelihood type to produce the posterior.

Source

STATG012 slides5 Example5.6 on Moodle at UCL STATG012 slides5

References

Bolstad, W.M. 2007. Introduction to Bayesian Statistics. (2nd ed.). Hoboken, New Jersey: John Wiley & Sons, Inc.

See Also

summary.g12post for summararies of prior and posterior distribution.

plot.g12post for plots of prior and posterior distribution.

Examples

## an observation of 10 with an exponential prior
a <- poisgamma(10, 1, 1)
summary(a)

## An Example 5.6 from slides 6, summary and plot it
x <- c(2, 10)
ex <- poisgamma(x, 4, 1)
summary(ex)
plot(ex,leg_pos = "right",cex = 1, lty = 5:6,
main = "Distributions of Example5.6")

yijin71/statg012 documentation built on May 23, 2019, 4:04 p.m.