@@ -180,9 +180,9 @@ Run _SAM2MAP_ without option to read the following documentation:
* By default, all sequenced bases with Phread score < 20 are not considered (option `-q`), therefore minimizing the impact of sequencing errors when computing the consensus sequence. By default, all read alignment with Phred score < 20 (as assessed by the read mapping program) are also not considered (option `-Q`), therefore discarding from the consensus sequence every region with low mappability (e.g. low complexity or repeated regions).
* _SAM2MAP_ estimates a Poisson+Negative Binomial (NB) theoretical distribution from the observed read coverage distribution, and writes the results into an output file (cov.txt file extension). <br>
The Poisson distribution is dedicated to observed (near-)zero read coverage distribution (called the coverage tail distribution into output files *.cov.txt). It is determined by the probability mass function (PMF) <b>P</b><sub><em>λ</em></sub>(<em>x</em>) = <em>λ</em><sup><em>x</em></sup><em>e</em><sup>-<em>λ</em></sup>Γ(<em>x</em>+1)<sup>-1</sup>, where Γ is the [gamma function](https://en.wikipedia.org/wiki/Gamma_function). <br>
The (main) NB distribution is used to determine the min/max coverage depths (as ruled by option `-p`) to assess reference regions where the consensus sequence can be trustingly built. The NB(<em>p</em>,<em>r</em>) distribution is determined by the PMF <b>P</b><sub><em>p</em>,<em>r</em></sub>(<em>x</em>) = Γ(<em>r</em>+<em>x</em>) Γ(<em>x</em>+1)<sup>-1</sup>Γ(<em>r</em>)<sup>-1</sup><em>p</em><sup><em>x</em></sup> (1-<em>p</em>)<sup><em>r</em></sup>. However, when the observed read coverage distribution is not overdispersed (i.e. the NB parameter <em>r</em> tends to infinity), the NB distribution is replaced by the Generalized Poisson (GP) one. The GP(<em>λ'</em>,<em>ρ</em>) distribution is here determined by the PMF <b>P</b><sub><em>λ'</em>,<em>ρ</em></sub>(<em>x</em>) = <em>λ'</em> (<em>λ'</em>+<em>ρx</em>)<sup><em>x</em>-1</sup><em>e</em><sup>-<em>λ'</em>-<em>ρx</em></sup>Γ(<em>x</em>+1)<sup>-1</sup>, where <em>ρ</em><0;when<em>ρ</em> = 0, GP(<em>λ'</em>,0) reduces to a Poisson distribution of parameter <em>λ'</em> (for more details, see e.g. Consul and Shoukri 1985). <br>
From the above formalizations, the Poisson+NB theoretical distribution is therefore determined by the PMF <em>w</em><b>P</b><sub><em>λ</em></sub>(<em>x</em>) + (1-<em>w</em>) <b>P</b><sub><em>p</em>,<em>r</em></sub>(<em>x</em>). The values of the different parameters <em>w</em>, <em>λ</em>, <em>p</em> and <em>r</em> are written into output files *.cov.txt. Of note, such statistical results can also be used jointly with a genome coverage profile analysis (e.g. Lindner et al. 2013).
The Poisson distribution is dedicated to observed (near-)zero read coverage distribution (called the coverage tail distribution into output files *.cov.txt). It is determined by the probability mass function (PMF) <b>P</b><sub><em>λ</em></sub>(<em>x</em>) = <em>λ</em><sup><em>x</em></sup><em>e</em><sup>-<em>λ</em></sup>Γ(<em>x</em>+1)<sup>-1</sup>, where Γ is the [gamma function](https://en.wikipedia.org/wiki/Gamma_function) and <em>λ</em>≤ 1. <br>
The (main) NB distribution is used to determine the min/max coverage depths (as ruled by option `-p`) to assess reference regions where the consensus sequence can be trustingly built. The NB(<em>p</em>,<em>r</em>) distribution is determined by the PMF <b>P</b><sub><em>p</em>,<em>r</em></sub>(<em>x</em>) = Γ(<em>r</em>+<em>x</em>) Γ(<em>x</em>+1)<sup>-1</sup>Γ(<em>r</em>)<sup>-1</sup><em>p</em><sup><em>x</em></sup> (1-<em>p</em>)<sup><em>r</em></sup>. However, when there is no overdispersion (i.e. the NB parameter <em>r</em> tends to infinity), the NB distribution is replaced by the Generalized Poisson (GP) one. The GP(<em>λ'</em>,<em>ρ</em>) distribution is here determined by the PMF <b>P</b><sub><em>λ'</em>,<em>ρ</em></sub>(<em>x</em>) = <em>λ'</em> (<em>λ'</em>+<em>ρx</em>)<sup><em>x</em>-1</sup><em>e</em><sup>-<em>λ'</em>-<em>ρx</em></sup>Γ(<em>x</em>+1)<sup>-1</sup>, where <em>ρ</em><0;when<em>ρ</em> = 0, GP(<em>λ'</em>,0) reduces to a Poisson distribution with parameter <em>λ'</em> (for more details, see e.g. Consul and Shoukri 1985). <br>
From the above formalizations, the Poisson+NB theoretical distribution is therefore determined by the PMF <em>w</em><b>P</b><sub><em>λ</em></sub>(<em>x</em>) + (1-<em>w</em>) <b>P</b><sub><em>p</em>,<em>r</em></sub>(<em>x</em>). The values of the different parameters <em>w</em>, <em>λ</em>, <em>p</em> and <em>r</em> are written into output files *.cov.txt. Of note, such statistical results can be useful when _SAM2MAP_ is used to perform a genome coverage profile analysis (e.g. Lindner et al. 2013).
