# 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.