## Binomial sampling with a beta prior

### Description

Evaluates and plots the posterior density for \pi, the probability of a success in a Bernoulli trial, with binomial sampling and a continous beta(a,b) prior.

### Usage

binobp(x, n, a = 1, b = 1, pi = seq(0, 1, by = 0.001), ...)


### Arguments

 x the number of observed successes in the binomial experiment. n the number of trials in the binomial experiment. a parameter for the beta prior - must be greater than zero b parameter for the beta prior - must be greater than zero pi A range of values for the prior to be calculated over. ... additional arguments that are passed to Bolstad.control

### Value

An object of class 'Bolstad' is returned. This is a list with the following components:

 prior the prior density of \pi, i.e. the beta(a,b) density likelihood the likelihood of x given \pi and n, i.e. the binomial(n,\pi) density posterior the posterior density of \pi given x and n - i.e. the beta(a+x,b+n-x) density pi the values of \pi for which the posterior density was evaluated mean the posterior mean var the posterior variance sd the posterior std. deviation quantiles a set of quantiles from the posterior cdf a cumulative distribution function for the posterior quantileFun a quantile function for the posterior

binodp binogcp

### Examples


## simplest call with 6 successes observed in 8 trials and a beta(1,1) uniform
## prior
binobp(6,8)

## 6 successes observed in 8 trials and a non-uniform beta(0.5,6) prior
binobp(6,8,0.5,6)

## 4 successes observed in 12 trials with a non uniform beta(3,3) prior
## plot the stored prior, likelihood and posterior
results = binobp(4, 12, 3, 3)
decomp(results)