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<h2>
<span class="refentrytitle">GEN21</span>
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<p>GEN21 —
Generates tables of different random distributions.
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<div class="refsect1" title="Description">
<a id="id3739901"></a>
<h2>Description</h2>
<p>
This generates tables of different random distributions. (See also <a class="link" href="betarand.html" title="betarand"><em class="citetitle">betarand</em></a>, <a class="link" href="bexprnd.html" title="bexprnd"><em class="citetitle">bexprnd</em></a>, <a class="link" href="cauchy.html" title="cauchy"><em class="citetitle">cauchy</em></a>, <a class="link" href="exprand.html" title="exprand"><em class="citetitle">exprand</em></a>, <a class="link" href="gauss.html" title="gauss"><em class="citetitle">gauss</em></a>, <a class="link" href="linrand.html" title="linrand"><em class="citetitle">linrand</em></a>, <a class="link" href="pcauchy.html" title="pcauchy"><em class="citetitle">pcauchy</em></a>, <a class="link" href="poisson.html" title="poisson"><em class="citetitle">poisson</em></a>, <a class="link" href="trirand.html" title="trirand"><em class="citetitle">trirand</em></a>, <a class="link" href="unirand.html" title="unirand"><em class="citetitle">unirand</em></a>, and <a class="link" href="weibull.html" title="weibull"><em class="citetitle">weibull</em></a>)
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<div class="refsect1" title="Syntax">
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<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 21 type level [arg1 [arg2]]</pre>
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<div class="refsect1" title="Initialization">
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<h2>Initialization</h2>
<p>
<span class="emphasis"><em>time</em></span> and <span class="emphasis"><em>size</em></span> are the usual GEN function arguments. <span class="emphasis"><em>level</em></span> defines the amplitude. Note that GEN21 is not self-normalizing as are most other GEN functions. <span class="emphasis"><em>type</em></span> defines the distribution to be used as follow:
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<p>1 = Uniform (positive numbers only)</p>
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<p>2 = Linear (positive numbers only)</p>
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<p>3 = Triangular (positive and negative numbers)</p>
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<p>4 = Exponential (positive numbers only)</p>
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<p>5 = Biexponential (positive and negative numbers)</p>
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<p>6 = Gaussian (positive and negative numbers)</p>
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<p>7 = Cauchy (positive and negative numbers)</p>
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<p>8 = Positive Cauchy (positive numbers only)</p>
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<p>9 = Beta (positive numbers only)</p>
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<p>10 = Weibull (positive numbers only)</p>
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<p>11 = Poisson (positive numbers only)</p>
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<p>
Of all these cases only 9 (Beta) and 10 (Weibull) need extra arguments. Beta needs two arguments and Weibull one.
</p>
<p>
If <span class="emphasis"><em>type</em></span> = 6, the random numbers in the ftable follow a normal distribution centered
around 0.0 (mu = 0.0) with a variance (sigma) of <span class="emphasis"><em>level</em></span> / 3.83. Thus more than 99.99%
of the random values generated are in the range -<span class="emphasis"><em>level</em></span> to +<span class="emphasis"><em>level</em></span>.
The default value for <span class="emphasis"><em>level</em></span> is 1 (sigma = 0.261).
If a mean value different of 0.0 is desired, this mean value has to be added to the generated numbers.
</p>
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<div class="refsect1" title="Examples">
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<h2>Examples</h2>
<p>
</p>
<div class="informalexample">
<pre class="programlisting">
<span class="stamnt">f</span>1 0 1024 21 1 <span class="comment">; Uniform (white noise)</span>
<span class="stamnt">f</span>1 0 1024 21 6 <span class="comment">; Gaussian (mu=0.0, sigma=1/3.83=0.261)</span>
<span class="stamnt">f</span>1 0 1024 21 6 5.745 <span class="comment">; Gaussian (mu=0.0, sigma=5.745/3.83=1.5)</span>
<span class="stamnt">f</span>1 0 1024 21 9 1 1 2 <span class="comment">; Beta (note that level precedes arguments)</span>
<span class="stamnt">f</span>1 0 1024 21 10 1 2 <span class="comment">; Weibull</span></pre>
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<p>
All of the above additions were designed by the author between May and December 1994, under the supervision of Dr. Richard Boulanger.
</p>
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<div class="refsect1" title="Credits">
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<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
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<td>Author: Paris Smaragdis</td>
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<td>MIT, Cambridge</td>
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<td>1995</td>
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<p>
</p>
<p>
</p>
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<td>Author: John ffitch</td>
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<td>University of Bath/Codemist Ltd.</td>
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<td>Bath, UK</td>
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<p>
</p>
<p>Precisions about mu and sigma added by François Pinot after a discussion with
Joachim Heintz on the Csound List, December 2010.</p>
<p>New in Csound version 3.2</p>
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