ShiftConvolve is a R package which uses exponential shifting and the Fast Fourier Transformations (FFT) to compute the (right) tail of distribution of the Poisson Binomial Distribution.
This package makes use of the minimalist Fast Fourier Transform library known as minFFT to perform the necessary DFT and Inverse DFT computations.
For the ShiftConvolve implementation which uses FFTW3 to perform the Fourier Transformations please go to https://github.com/andrew12678/ShiftConvolveFFTW.
In the interest of speed we all significant computational aspects of our procedure are executed by code written in C and the R code mainly acts as a wrapper around that compiled C code.
We have successfully installed ShiftConvolveFFTW on Windows 10: Professional Version 1909, macOS: Mojave 10.14.6/Catalina 10.15.4 and Linux: Ubuntu 18.04/Manjaro 19.02 KDE Plasma. A full installation guide will be provided below for all 3 Operating Systems.
ShiftConvolveFFTW has also been installed on both AMD and Intel CPU systems. Specifically, a Intel Core i7 MacMini with 32GB of RAM, AMD Ryzen 5 2600 with 16GB of RAM and a Macbook Pro i7 with 16GB of RAM
There are no external dependencies required to be installed for this version of ShiftConvolve. The required minFFT files have been compiled and included into the ShiftConvolve project.
Windows users may be required (instructed by compilation errors later anyways) to install Rtools from the following website https://cran.r-project.org/bin/windows/Rtools/. Make sure to tick the box saying 'Add to system path variables' when installing.
The most simple installation involves simply cloning this repository and installing ShiftConvolve from source.
install.packages('devtools') # If you have not installed devtools
devtools::install_github('https://github.com/andrew12678/ShiftConvolve.git')An alternative installation procedure involves cloning the repository, creating a RStudio project and then building.
An simple example with the uniform distribution
library(ShiftConvolvePoibin)
set.seed(18)
n=1000
probs <- runif(n)
x <- c(200, 500, 800)
p <- seq(0, 1, 0.01)
dpoisbin(x,probs,method="ShiftConvolve",log.p=FALSE)
ppoisbin(x,probs,method="ShiftConvolve",lower.tail=FALSE,log.p=TRUE)
qpoisbin(p,probs,method="ShiftConvolve",lower.tail=TRUE,log.p=FALSE)
rpoisbin(n,probs)[1] Peres, N., Lee, A., and Keich, U. (2020). Exactly computing the tail of the Poisson-Binomial Distribution. arXiv:2004.07429