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<h1 class="title toc-ignore">Usage with Rcpp</h1>



<p>Each procedure’s probability mass function (PMF) and cumulative
distribution function (CDF) was implemented in <em>C++</em> using the
<code>Rcpp</code> package. By means of <code>Rcpp::interface</code>,
these functions are exported to both the package’s <em>R</em> namespace
and <em>C++</em> headers. That way, the following functions can then be
used by other packages that use <code>Rcpp</code>:</p>
<pre><code>/***   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 &amp; 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);</code></pre>
<div id="making-the-functions-usable" class="section level2">
<h2>Making the functions usable</h2>
<p>There are only a few simple steps to follow:</p>
<ol style="list-style-type: decimal">
<li>Add the <code>Rcpp</code> and <code>PoissonBinomial</code> packages
to the <code>Imports</code> and <code>LinkingTo</code> fields of the
<code>DESCRIPTION</code> file.</li>
<li>Add <code>#include &lt;PoissonBinomial.h&gt;</code> to source
(<code>.cpp</code>) and/or header (<code>.h</code>, <code>.hpp</code>)
files in which these functions are to be used.</li>
<li>Optional: Add <code>using namespace PoissonBinomial;</code>. Without
it, the use of functions of this package must be fully qualified with
<code>PoissonBinomial::</code>,
e.g. <code>PoissonBinomial::dpb_dc</code> instead of
<code>dpb_dc</code></li>
</ol>
</div>
<div id="important-remarks" class="section level2">
<h2>Important Remarks</h2>
<p>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
<em>R</em> or <em>C/C++</em> functions. It must be made sure that</p>
<ul>
<li>the observations in the <code>obs</code> vectors are valid,</li>
<li>the probabilities in the <code>probs</code> vector are in <span class="math inline">\((0, 1)\)</span> and</li>
<li>for <code>dpb_gmba</code>, <code>ppb_gmba</code>,
<code>dpb_na</code>, <code>ppb_na</code>, <code>dgpb_na</code> and
<code>pgpb_na</code>: the probabilities in the <code>probs</code> vector
<strong>must not</strong> contain zeros or ones.</li>
</ul>
<p>Furthermore, the CDFs only compute non-logarithmic probabilities. If
logarithms are needed, they must be computed “manually”.</p>
</div>



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