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---
title: "Usage with Rcpp"
output: rmarkdown::html_vignette
vignette: >
%\VignetteIndexEntry{Usage with Rcpp}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
---
```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
```
Each procedure's probability mass function (PMF) and cumulative distribution function (CDF) was implemented in *C++* using the `Rcpp` package. By means of `Rcpp::interface`, these functions are exported to both the package's *R* namespace and *C++* headers. That way, the following functions can then be used by other packages that use `Rcpp`:
```
/*** Ordinary Poisson Binomial Distribution ***/
/*** Exact Procedures ***/
// Direct Convolution (DC)
// PMF
NumericVector dpb_conv(const IntegerVector obs,
const NumericVector probs);
// CDF
NumericVector ppb_conv(const IntegerVector obs,
const NumericVector probs,
const bool lower_tail);
// Divide & Conquer FFT Tree Convolution (DC-FFT)
// PMF
NumericVector dpb_dc(const IntegerVector obs,
const NumericVector probs);
// CDF
NumericVector ppb_dc(const IntegerVector obs,
const NumericVector probs,
const bool lower_tail);
// Discrete Fourier Transformation of the Characteristic Function (DFT-CF)
// PMF
NumericVector dpb_dftcf(const IntegerVector obs,
const NumericVector probs);
// CDF
NumericVector ppb_dftcf(const IntegerVector obs, const NumericVector probs,
const bool lower_tail);
// Recursive Formula (RF)
// PMF
NumericVector dpb_rf(const IntegerVector obs,
const NumericVector probs);
// CDF
NumericVector ppb_rf(const IntegerVector obs,
const NumericVector probs,
const bool lower_tail);
/*** Approximations ***/
// Arithmetic Mean Binomial Approximation (AMBA)
// PMF
NumericVector dpb_mean(const IntegerVector obs,
const NumericVector probs);
// CDF
NumericVector ppb_mean(const IntegerVector obs,
const NumericVector probs,
const bool lower_tail);
// Geometric Mean Binomial Approximations (GMBA)
// PMF
NumericVector dpb_gmba(const IntegerVector obs,
const NumericVector const probs,
const bool anti);
// CDF
NumericVector ppb_gmba(const IntegerVector obs,
const NumericVector probs,
const bool anti,
const bool lower_tail);
// Poisson Approximation (PA)
// PMF
NumericVector dpb_pa(const IntegerVector obs,
const NumericVector probs);
// CDF
NumericVector ppb_pa(const IntegerVector obs,
const NumericVector probs,
const bool lower_tail);
// Normal Approximations (NA, RNA)
// PMF
NumericVector dpb_na(const IntegerVector obs,
const NumericVector probs,
const bool refined);
// CDF
NumericVector ppb_na(const IntegerVector obs,
const NumericVector probs,
const bool refined,
const bool lower_tail);
/*** Generalized Poisson Binomial Distribution ***/
/*** Exact Procedures ***/
// Generalized Direct Convolution (G-DC)
// PMF
NumericVector dgpb_conv(const IntegerVector obs,
const NumericVector probs,
const NumericVector val_p,
const NumericVector val_q);
// CDF
NumericVector pgpb_conv(const IntegerVector obs,
const NumericVector probs,
const NumericVector val_p,
const NumericVector val_q,
const bool lower_tail);
// Generalized Discrete Fourier Transformation of the Characteristic Function (G-DFT-CF)
// PMF
NumericVector dgpb_dftcf(const IntegerVector obs,
const NumericVector probs,
const NumericVector val_p,
const NumericVector val_q);
// CDF
NumericVector pgpb_dftcf(const IntegerVector obs,
const NumericVector probs,
const NumericVector val_p,
const NumericVector val_q,
const bool lower_tail);
/*** Approximations ***/
// Generalized Normal Approximations (G-NA, G-RNA)
// PMF
NumericVector dgpb_na(const IntegerVector obs,
const NumericVector probs,
const NumericVector val_p,
const NumericVector val_q,
const bool refined,
const bool lower_tail);
// CDF
NumericVector pgpb_na(const IntegerVector obs,
const NumericVector probs,
const NumericVector val_p,
const NumericVector val_q,
const bool refined,
const bool lower_tail);
```
## Making the functions usable
There are only a few simple steps to follow:
1. Add the `Rcpp` and `PoissonBinomial` packages to the `Imports` and `LinkingTo` fields of the `DESCRIPTION` file.
2. Add `#include <PoissonBinomial.h>` to source (`.cpp`) and/or header (`.h`, `.hpp`) files in which these functions are to be used.
3. Optional: Add `using namespace PoissonBinomial;`. Without it, the use of functions of this package must be fully qualified with `PoissonBinomial::`, e.g. `PoissonBinomial::dpb_dc` instead of `dpb_dc`
## Important Remarks
For better performance, the PMFs and CDFs do not check any of their parameters for plausibility! This must be done by the user by means of *R* or *C/C++* functions. It must be made sure that
* the observations in the `obs` vectors are valid,
* the probabilities in the `probs` vector are in $(0, 1)$ and
* for `dpb_gmba`, `ppb_gmba`, `dpb_na`, `ppb_na`, `dgpb_na` and `pgpb_na`: the probabilities in the `probs` vector **must not** contain zeros or ones.
Furthermore, the CDFs only compute non-logarithmic probabilities. If logarithms are needed, they must be computed "manually".
|
