summarize_gamma_poisson {bayesrules}

Summarize the Gamma-Poisson Model

Description

Consider a Gamma-Poisson Bayesian model for rate parameter \lambda with a Gamma(shape, rate) prior on \lambda and a Poisson likelihood for the data. Given information on the prior (shape and rate) and data (the sample size n and sum_y), this function summarizes the mean, mode, and variance of the prior and posterior Gamma models of \lambda.

Usage

summarize_gamma_poisson(shape, rate, sum_y = NULL, n = NULL)

Arguments

shape

positive shape parameter of the Gamma prior

rate

positive rate parameter of the Gamma prior

sum_y

sum of observed data values for the Poisson likelihood

n

number of observations for the Poisson likelihood

Value

data frame

Examples

summarize_gamma_poisson(shape = 3, rate = 4, sum_y = 7, n = 12)