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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2000 - INRIA - Carlos Klimann
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
-->
<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="cdfbin">
<refnamediv>
<refname>cdfbin</refname>
<refpurpose> cumulative distribution function Binomial distribution</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[P,Q]=cdfbin("PQ",S,Xn,Pr,Ompr)
[S]=cdfbin("S",Xn,Pr,Ompr,P,Q)
[Xn]=cdfbin("Xn",Pr,Ompr,P,Q,S)
[Pr,Ompr]=cdfbin("PrOmpr",P,Q,S,Xn)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>P,Q,S,Xn,Pr,Ompr</term>
<listitem>
<para>six real vectors of the same size.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>P,Q (Q=1-P) </term>
<listitem>
<para>The cumulation from 0 to S of the binomial distribution. (Probablility of S or fewer successes in XN trials each with probability of success PR.) Input range: [0,1].</para>
</listitem>
</varlistentry>
<varlistentry>
<term>S</term>
<listitem>
<para>The number of successes observed. Input range: [0, XN] Search range: [0, XN]</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Xn</term>
<listitem>
<para>The number of binomial trials. Input range: (0, +infinity). Search range: [1E-300, 1E300]</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Pr,Ompr (Ompr=1-Pr) </term>
<listitem>
<para>The probability of success in each binomial trial. Input range: [0,1]. Search range: [0,1]</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Calculates any one parameter of the binomial
distribution given values for the others.
</para>
<para>
Formula 26.5.24 of Abramowitz and Stegun, Handbook of
Mathematical Functions (1966) is used to reduce the binomial
distribution to the cumulative incomplete beta distribution.
</para>
<para>
Computation of other parameters involve a seach for a value that
produces the desired value of P. The search relies on the
monotinicity of P with the other parameter.
</para>
<para>
From DCDFLIB: Library of Fortran Routines for Cumulative Distribution
Functions, Inverses, and Other Parameters (February, 1994)
Barry W. Brown, James Lovato and Kathy Russell. The University of
Texas.
</para>
</refsection>
</refentry>
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