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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”.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.