summarize_gamma_poisson function

Summarize the Gamma-Poisson Model

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 $\lambda$.

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

Returns

data frame

Examples

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