poiss {plpoisson}

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)

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.

Details

Prediction bounds are obtained through the binary search algorithm.

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.

Author(s)

Valbona Bejleri, Luca Sartore and Balgobin Nandram

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