plpoisson (version 0.3.1)

poiss: Frequentist Prediction Limits for Poisson Distribution

Description

The function provides the frequentist prediction limits of a Poisson random variable. The resulting prediction bounds quantify the uncertainty associated to the predicted future number of occurences in a time windows of size \(t\).

Usage

poiss(xobs, n, s, t, alpha = 0.05)

Value

A list containing the following components:

lower

An integer value representing the lower bound of the prediction limit.

upper

An integer value representing the upper bound of the prediction limit.

Arguments

xobs

a numeric value denoting the number of the observed occurrencies.

n

a numeric value representing the total number of the time windows s in the past (observed time windows).

s

a numeric value corresponding to the fixed size (or average size) of the observed time windows.

t

a numeric value indicating the size of the future time window.

alpha

a numeric value associated to the probability of prediction. By default alpha = 0.05, thus a prediction interval at 95% will be returned.

Author

Valbona Bejleri, Luca Sartore and Balgobin Nandram

Details

Prediction bounds are obtained through the binary search algorithm.

References

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

Davis, C. H. (1969). The binary search algorithm. American Documentation (pre-1986), 20(2), 167.

See Also

poisBayes, poisJEFF, poisUNIF

Examples

# Loading the package
library(plpoisson)
set.seed(2020L)

# Number of observed time windows
n <- 555L

# Simulating a dataset
data <- cbind.data.frame(
    occ_obs = rpois(n, rgamma(n, 5.5, .5)),
    win_siz = rgamma(n, 1.44, .777)
) 

## Frequentist prediction limits
poiss(sum(data$occ_obs), # Past occurrencies 
    nrow(data), # Total past time windows
    mean(data$win_siz), # Window size
    3) # Size of future window