nbinombeta: Negative binomial sampling distribution with a beta...

In yijin71/statg012: statg012: Statistical Inference at UCL

Description

Define the posterior distribution function for π ( θ | k ), with a beta prior distribution π ( θ; α, β ) and a negative binomial sampling distribution p ( k | θ ).

Usage

nbinombeta(alpha = 1, beta = 1, k, r, theta = seq(0, 1, 0.001))

Arguments

alpha	the parameter for the beta distribution ( ≥ 0 ).
beta	the parameter for the beta distribution ( ≥ 0 ).
k	the number of failures in rth successes
r	the rth successes.
theta	the range of the probability of success.

Value

An object of class "g12post" is returned.

prior	the prior distribution, i.e. the beta(α,β) distribution.
likelihood	the likelihood function of k given θ, i.e. the nbinomial(r,θ) distribution.
posterior	the posterior distribution of θ given k, i.e. the beta(α+r, β+k) distribution.
theta	the range of the probability of success.
pri.alpha	the alpha parameter for the beta distribution of prior.
pri.beta	the beta parameter for the beta distribution of prior.
pos.alpha	the alpha parameter for the beta distribution of posterior.
pos.beta	the beta parameter for the beta distribution of posterior.
model	the prior and likelihood type to produce the posterior.

Source

For the theory, based on

The STATG012 slides2 Example3.6 on Moodle at UCL.

STATG012 slides2

References

Cook, JD. 2009. Notes on the Negative Binomial Distribution. Available from: reference link.

See Also

summary.g12post for summararies of prior and posterior distribution.

plot.g12post for plots of prior and posterior distribution.

Examples

## example : 3 failures before the 2th successes and a beta(4,6) prior.
ex <- nbinombeta(4, 6, 3, 2)
## summary and plot the above example
summary(ex)
plot(ex,lty = 2:3, col = c(5,2))

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