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)
NumericVector dpb_conv(IntegerVector obs, NumericVector probs);                     // PMF
NumericVector ppb_conv(IntegerVector obs, NumericVector probs);                     // CDF

// Divide & Conquer FFT Tree Convolution (DC-FFT)
NumericVector dpb_dc(IntegerVector obs, NumericVector probs);                       // PMF
NumericVector ppb_dc(IntegerVector obs, NumericVector probs);                       // CDF

// Discrete Fourier Transformation of the Characteristic Function (DFT-CF)
NumericVector dpb_dftcf(IntegerVector obs, NumericVector probs);                    // PMF
NumericVector ppb_dftcf(IntegerVector obs, NumericVector probs);                    // CDF

// Recursive Formula (RF)
NumericVector dpb_rf(IntegerVector obs, NumericVector probs);                       // PMF
NumericVector ppb_rf(IntegerVector obs, NumericVector probs);                       // CDF


/***   Approximations   ***/

// Arithmetic Mean Binomial Approximation (AMBA)
NumericVector dpb_mean(IntegerVector obs, NumericVector probs);                     // PMF
NumericVector ppb_mean(IntegerVector obs, NumericVector probs);                     // CDF

// Geometric Mean Binomial Approximations (GMBA)
NumericVector dpb_gmba(IntegerVector obs, NumericVector probs, bool anti);          // PMF
NumericVector ppb_gmba(IntegerVector obs, NumericVector probs, bool anti);          // CDF

// Poisson Approximation (PA)
NumericVector dpb_pa(IntegerVector obs, NumericVector probs);                       // PMF
NumericVector ppb_pa(IntegerVector obs, NumericVector probs);                       // CDF

// Normal Approximations (NA, RNA)
NumericVector dpb_na(IntegerVector obs, NumericVector probs, bool refined);         // PMF
NumericVector ppb_na(IntegerVector obs, NumericVector probs, bool refined);         // CDF



/***   Generalized Poisson Binomial Distribution   ***/


/***   Exact Procedures   ***/

// Generalized Direct Convolution (G-DC)
NumericVector dgpb_conv(IntegerVector obs,   NumericVector probs,
                        NumericVector val_p, NumericVector val_q);                  // PMF
NumericVector pgpb_conv(IntegerVector obs,   NumericVector probs,
                        NumericVector val_p, NumericVector val_q);                  // CDF

// Generalized Discrete Fourier Transformation of the Characteristic Function (G-DFT-CF)
NumericVector dgpb_dftcf(IntegerVector obs,  NumericVector probs,
                         NumericVector val_p, NumericVector val_q);                 // PMF
NumericVector pgpb_dftcf(IntegerVector obs,  NumericVector probs,
                         NumericVector val_p, NumericVector val_q);                 // CDF
                       
                       
/***   Approximations   ***/

// Generalized Normal Approximations (G-NA, G-RNA)
NumericVector dgpb_na(IntegerVector obs,  NumericVector probs,
                      NumericVector val_p, NumericVector val_q, bool refined);      // PMF
NumericVector pgpb_na(IntegerVector obs,  NumericVector probs,
                      NumericVector val_p, NumericVector val_q, bool refined);      // CDF

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

Furthermore, the CDFs only compute lower-tail cumulative probabilities, i.e. \(P(X \leq k)\). If upper-tail probabilities \(P(X > k)\) are needed, they must be computed “manually”. The same applies for logarithmic probabilities, which can be calculated using Rcpp::log for instance.