Usage with Rcpp

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:

Add the Rcpp and PoissonBinomial packages to the Imports and LinkingTo fields of the DESCRIPTION file.
Add #include <PoissonBinomial.h> to source (.cpp) and/or header (.h, .hpp) files in which these functions are to be used.
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”.