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<title>CDF function for BETA Distribution. Calculates any one parameter of the beta distribution given values for the others.</title>
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<div class="refnamediv">
<h1 class="refname">stats_cdf_beta</h1>
<p class="verinfo">(PECL stats >= 1.0.0)</p><p class="refpurpose"><span class="refname">stats_cdf_beta</span> — <span class="dc-title">CDF function for BETA Distribution. Calculates any one parameter of the beta distribution given values for the others.</span></p>
</div>
<div class="refsect1 description" id="refsect1-function.stats-cdf-beta-description">
<h3 class="title">Description</h3>
<div class="methodsynopsis dc-description">
<span class="type">float</span> <span class="methodname"><strong>stats_cdf_beta</strong></span>
( <span class="methodparam"><span class="type">float</span> <code class="parameter">$par1</code></span>
, <span class="methodparam"><span class="type">float</span> <code class="parameter">$par2</code></span>
, <span class="methodparam"><span class="type">float</span> <code class="parameter">$par3</code></span>
, <span class="methodparam"><span class="type">int</span> <code class="parameter">$which</code></span>
)</div>
<p class="para rdfs-comment">
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
monotonicity 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.
</p>
</div>
<div class="refsect1 parameters" id="refsect1-function.stats-cdf-beta-parameters">
<h3 class="title">Parameters</h3>
<p class="para">
<dl>
<dt>
<span class="term"><em><code class="parameter">par1</code></em></span>
<dd>
<p class="para">
</p>
</dd>
</dt>
<dt>
<span class="term"><em><code class="parameter">par2</code></em></span>
<dd>
<p class="para">
</p>
</dd>
</dt>
<dt>
<span class="term"><em><code class="parameter">par3</code></em></span>
<dd>
<p class="para">
</p>
</dd>
</dt>
<dt>
<span class="term"><em><code class="parameter">which</code></em></span>
<dd>
<p class="para">
Integer indicating which of the next four argument
values is to be calculated from the others.
Legal range: 1..4
which = 1 : Calculate P and Q from X,Y,A and B
which = 2 : Calculate X and Y from P,Q,A and B
which = 3 : Calculate A from P,Q,X,Y and B
which = 4 : Calculate B from P,Q,X,Y and A
</p>
</dd>
</dt>
</dl>
</p>
</div>
<div class="refsect1 returnvalues" id="refsect1-function.stats-cdf-beta-returnvalues">
<h3 class="title">Return Values</h3>
<p class="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
</p>
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