php-doc-en/reference/stats/functions/stats-cdf-beta.xml

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<refentry id="function.stats-cdf-beta">
 <refnamediv>
  <refname>stats_cdf_beta</refname>
  <refpurpose>CDF function for BETA Distribution. Calculates any one parameter of the beta distribution given values for the others.</refpurpose>
 </refnamediv>
 <refsect1 role="description">
  &reftitle.description;
  <methodsynopsis>
   <type>float</type><methodname>stats_cdf_beta</methodname>
   <methodparam><type>float</type><parameter>par1</parameter></methodparam>
   <methodparam><type>float</type><parameter>par2</parameter></methodparam>
   <methodparam><type>float</type><parameter>par3</parameter></methodparam>
   <methodparam><type>int</type><parameter>which</parameter></methodparam>
  </methodsynopsis>
  <para>

                              Method

     Cumulative distribution function  (P)  is calculated directly by
     code associated with the following reference.

     DiDinato, A. R. and Morris,  A.   H.  Algorithm 708: Significant
     Digit Computation of the Incomplete  Beta  Function Ratios.  ACM
     Trans. Math.  Softw. 18 (1993), 360-373.

     Computation of other parameters involve a search for a value that
     produces  the desired  value  of P.   The search relies  on  the
     monotinicity of P with the other parameter.

                              Note

     The beta density is proportional to
               t^(A-1) * (1-t)^(B-1)

                              Arguments


     P -- The integral from 0 to X of the chi-square
            distribution.
            Input range: [0, 1].

     Q -- 1-P.
            Input range: [0, 1].
            P + Q = 1.0.

     X -- Upper limit of integration of beta density.
            Input range: [0,1].
            Search range: [0,1]

     Y -- 1-X.
            Input range: [0,1].
            Search range: [0,1]
            X + Y = 1.0.

     A -- The first parameter of the beta density.
            Input range: (0, +infinity).
            Search range: [1D-100,1D100]

     B -- The second parameter of the beta density.
            Input range: (0, +infinity).
            Search range: [1D-100,1D100]

     STATUS  -- 0 if calculation completed correctly
               -I if input parameter number I is out of range
                1 if answer appears to be lower than lowest
                  search bound
                2 if answer appears to be higher than greatest
                  search bound
                3 if P + Q .ne. 1
                4 if X + Y .ne. 1

     BOUND  -- Undefined if STATUS is 0

               Bound exceeded by parameter number I if STATUS
               is negative.

               Lower search bound if STATUS is 1.

               Upper search bound if STATUS is 2.

  </para>

 </refsect1>
 <refsect1 role="parameters">
  &reftitle.parameters;
  <para>
   <variablelist>
    <varlistentry>
     <term><parameter>par1</parameter></term>
     <listitem>
      <para>
       Its description
      </para>
     </listitem>
    </varlistentry>
    <varlistentry>
     <term><parameter>par2</parameter></term>
     <listitem>
      <para>
       Its description
      </para>
     </listitem>
    </varlistentry>
    <varlistentry>
     <term><parameter>par3</parameter></term>
     <listitem>
      <para>
       Its description
      </para>
     </listitem>
    </varlistentry>
    <varlistentry>
     <term><parameter>which</parameter></term>
     <listitem>
      <para>
      Integer indicating which of the next four argument
               values is to be calculated from the others.
               Legal range: 1..4
               iwhich = 1 : Calculate P and Q from X,Y,A and B
               iwhich = 2 : Calculate X and Y from P,Q,A and B
               iwhich = 3 : Calculate A from P,Q,X,Y and B
               iwhich = 4 : Calculate B from P,Q,X,Y and A

      </para>
     </listitem>
    </varlistentry>
   </variablelist>
  </para>
 </refsect1>
 <refsect1 role="returnvalues">
  &reftitle.returnvalues;
  <para>
     STATUS  -- 0 if calculation completed correctly
               -I if input parameter number I is out of range
                1 if answer appears to be lower than lowest
                  search bound
                2 if answer appears to be higher than greatest
                  search bound
                3 if P + Q .ne. 1
                4 if X + Y .ne. 1
  </para>
 </refsect1>

 <!-- Use when ERRORS exist
 <refsect1 role="errors">
  &reftitle.errors;
  <para>
   When does this function throw E_* level errors, or exceptions?
  </para>
 </refsect1>
 -->


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 <refsect1 role="changelog">
  &reftitle.changelog;
  <para>
   <informaltable>
    <tgroup cols="2">
     <thead>
      <row>
       <entry>&Version;</entry>
       <entry>&Description;</entry>
      </row>
     </thead>
     <tbody>
      <row>
       <entry>Enter the PHP version of change here</entry>
       <entry>Description of change</entry>
      </row>
     </tbody>
    </tgroup>
   </informaltable>
  </para>
 </refsect1>
 -->


 <!-- Use when examples exist
 <refsect1 role="examples">
  &reftitle.examples;
  <para>
   <example>
    <title>A <function>stats_cdf_beta</function> example</title>
    <para>
     Any text that describes the purpose of the example, or
     what goes on in the example should go here (inside the
     <example> tag, not out
    </para>
    <programlisting role="php">
<![CDATA[
<?php
if ($anexample === true) {
    echo 'Use the PEAR Coding Standards';
}
?>
]]>
    </programlisting>
    &example.outputs;
    <screen>
<![CDATA[
Use the PEAR Coding Standards
]]>
    </screen>
   </example>
  </para>
 </refsect1>
 -->


 <!-- Use when adding See Also links
 <refsect1 role="seealso">
  &reftitle.seealso;
  <para>
   <simplelist>
    <member><function></function></member>
    <member>Or <link linkend="somethingelse">something else</link></member>
   </simplelist>
  </para>
 </refsect1>
 -->


</refentry>

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