Prediction Limits for Poisson Distribution

Prediction limits for the Poisson distribution are produced from both frequentist and Bayesian viewpoints. Limiting results are provided in a Bayesian setting with uniform, Jeffreys and gamma as prior distributions. More details on the methodology are discussed in Bejleri and Nandram (2018) and Bejleri, Sartore and Nandram (2021) .

plpoisson: Prediction Limits for the Poisson Distribution

Authors

Valbona Bejleri, Luca Sartore and Balgobin Nandram

Maintainer: Luca Sartore

Features of the package

Prediction limits for Poisson distribution are useful when predicting the occurrences of some real life phenomena; in fact, these limits quantify the uncertainty associated with the predicted values. The plpoisson package provides a set of functions to compute prediction limits of the inferred Poisson distribution under both frequentist and Bayesian frameworks.

For a complete list of exported functions, use library(help = "plpoisson") once the plpoisson package is installed (see the inst/INSTALL.md file for a detailed description of the setup process).

Example

## Loading the package
library(plpoisson)

## Setting quantities of interest
xobs <- rpois(1, 50)    # Number of the observed occurrencies  
n <- 1                  # Total number of the time windows of
                        #   of size 's' observed in the past
s <- rgamma(1, 4, .567) # Fixed size of observed time windows
t <- rgamma(1, 3, .33)  # Future time window
a <- 5                  # Shape hyperparameter of a gamma prior
b <- 1.558              # Rate hyperparameter of a gamma prior

## Frequentist prediction limits
poiss(xobs, n, s, t)

## Bayesian prediction limits (with uniform prior)
poisUNIF(xobs, n, s, t)

## Bayesian prediction limits (with Jeffreys prior)
poisJEFF(xobs, n, s, t)

## Bayesian prediction limits (with gamma prior)
poisBayes(xobs, n, s, t, a, b)

References

Bejleri, V. (2005). Bayesian Prediction Intervals for the Poisson Model, Noninformative Priors, Ph.D. Dissertation, American University, Washington, DC.

Bejleri, V., & Nandram, B. (2018). Bayesian and frequentist prediction limits for the Poisson distribution. Communications in Statistics-Theory and Methods, 47(17), 4254-4271.

Bejleri, V., Sartore, L. & Nandram, B. (2021). Asymptotic equivalence between frequentist and Bayesian prediction limits for the Poisson distribution. Journal of the Korean Statistical Society doi:10.1007/s42952-021-00157-x