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<a name="Random-Number-Distribution-Examples"></a>
<div class="header">
<p>
Next: <a href="Random-Number-Distribution-References-and-Further-Reading.html#Random-Number-Distribution-References-and-Further-Reading" accesskey="n" rel="next">Random Number Distribution References and Further Reading</a>, Previous: <a href="Shuffling-and-Sampling.html#Shuffling-and-Sampling" accesskey="p" rel="previous">Shuffling and Sampling</a>, Up: <a href="Random-Number-Distributions.html#Random-Number-Distributions" accesskey="u" rel="up">Random Number Distributions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Examples-13"></a>
<h3 class="section">20.40 Examples</h3>

<p>The following program demonstrates the use of a random number generator
to produce variates from a distribution.  It prints 10 samples from the
Poisson distribution with a mean of 3.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;gsl/gsl_rng.h&gt;
#include &lt;gsl/gsl_randist.h&gt;

int
main (void)
{
  const gsl_rng_type * T;
  gsl_rng * r;

  int i, n = 10;
  double mu = 3.0;

  /* create a generator chosen by the 
     environment variable GSL_RNG_TYPE */

  gsl_rng_env_setup();

  T = gsl_rng_default;
  r = gsl_rng_alloc (T);

  /* print n random variates chosen from 
     the poisson distribution with mean 
     parameter mu */

  for (i = 0; i &lt; n; i++) 
    {
      unsigned int k = gsl_ran_poisson (r, mu);
      printf (&quot; %u&quot;, k);
    }

  printf (&quot;\n&quot;);
  gsl_rng_free (r);
  return 0;
}
</pre></div>

<p>If the library and header files are installed under <samp>/usr/local</samp>
(the default location) then the program can be compiled with these
options,
</p>
<div class="example">
<pre class="example">$ gcc -Wall demo.c -lgsl -lgslcblas -lm
</pre></div>

<p>Here is the output of the program,
</p>
<div class="example">
<pre class="example">$ ./a.out 
</pre><pre class="verbatim"> 2 5 5 2 1 0 3 4 1 1
</pre></div>

<p>The variates depend on the seed used by the generator.  The seed for the
default generator type <code>gsl_rng_default</code> can be changed with the
<code>GSL_RNG_SEED</code> environment variable to produce a different stream
of variates,
</p>
<div class="example">
<pre class="example">$ GSL_RNG_SEED=123 ./a.out 
</pre><pre class="verbatim"> 4 5 6 3 3 1 4 2 5 5
</pre></div>

<p>The following program generates a random walk in two dimensions.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;gsl/gsl_rng.h&gt;
#include &lt;gsl/gsl_randist.h&gt;

int
main (void)
{
  int i;
  double x = 0, y = 0, dx, dy;

  const gsl_rng_type * T;
  gsl_rng * r;

  gsl_rng_env_setup();
  T = gsl_rng_default;
  r = gsl_rng_alloc (T);

  printf (&quot;%g %g\n&quot;, x, y);

  for (i = 0; i &lt; 10; i++)
    {
      gsl_ran_dir_2d (r, &amp;dx, &amp;dy);
      x += dx; y += dy; 
      printf (&quot;%g %g\n&quot;, x, y);
    }

  gsl_rng_free (r);
  return 0;
}
</pre></div>

<p>Here is some output from the program, four 10-step random walks from the origin,
</p>

<p>The following program computes the upper and lower cumulative
distribution functions for the standard normal distribution at
<em>x=2</em>.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;gsl/gsl_cdf.h&gt;

int
main (void)
{
  double P, Q;
  double x = 2.0;

  P = gsl_cdf_ugaussian_P (x);
  printf (&quot;prob(x &lt; %f) = %f\n&quot;, x, P);

  Q = gsl_cdf_ugaussian_Q (x);
  printf (&quot;prob(x &gt; %f) = %f\n&quot;, x, Q);

  x = gsl_cdf_ugaussian_Pinv (P);
  printf (&quot;Pinv(%f) = %f\n&quot;, P, x);

  x = gsl_cdf_ugaussian_Qinv (Q);
  printf (&quot;Qinv(%f) = %f\n&quot;, Q, x);

  return 0;
}
</pre></div>

<p>Here is the output of the program,
</p>
<div class="example">
<pre class="verbatim">prob(x &lt; 2.000000) = 0.977250
prob(x &gt; 2.000000) = 0.022750
Pinv(0.977250) = 2.000000
Qinv(0.022750) = 2.000000
</pre></div>

<hr>
<div class="header">
<p>
Next: <a href="Random-Number-Distribution-References-and-Further-Reading.html#Random-Number-Distribution-References-and-Further-Reading" accesskey="n" rel="next">Random Number Distribution References and Further Reading</a>, Previous: <a href="Shuffling-and-Sampling.html#Shuffling-and-Sampling" accesskey="p" rel="previous">Shuffling and Sampling</a>, Up: <a href="Random-Number-Distributions.html#Random-Number-Distributions" accesskey="u" rel="up">Random Number Distributions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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