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<title>The Gaussian Distribution - GNU Scientific Library -- Reference Manual</title>
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<p>
<a name="The-Gaussian-Distribution"></a>
Next: <a rel="next" accesskey="n" href="The-Gaussian-Tail-Distribution.html">The Gaussian Tail Distribution</a>,
Previous: <a rel="previous" accesskey="p" href="Random-Number-Distribution-Introduction.html">Random Number Distribution Introduction</a>,
Up: <a rel="up" accesskey="u" href="Random-Number-Distributions.html">Random Number Distributions</a>
<hr>
</div>
<h3 class="section">19.2 The Gaussian Distribution</h3>
<div class="defun">
— Function: double <b>gsl_ran_gaussian</b> (<var>const gsl_rng * r, double sigma</var>)<var><a name="index-gsl_005fran_005fgaussian-1578"></a></var><br>
<blockquote><p><a name="index-Gaussian-distribution-1579"></a>This function returns a Gaussian random variate, with mean zero and
standard deviation <var>sigma</var>. The probability distribution for
Gaussian random variates is,
<pre class="example"> p(x) dx = {1 \over \sqrt{2 \pi \sigma^2}} \exp (-x^2 / 2\sigma^2) dx
</pre>
<p class="noindent">for x in the range -\infty to +\infty. Use the
transformation z = \mu + x on the numbers returned by
<code>gsl_ran_gaussian</code> to obtain a Gaussian distribution with mean
\mu. This function uses the Box-Mueller algorithm which requires two
calls to the random number generator <var>r</var>.
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_ran_gaussian_pdf</b> (<var>double x, double sigma</var>)<var><a name="index-gsl_005fran_005fgaussian_005fpdf-1580"></a></var><br>
<blockquote><p>This function computes the probability density p(x) at <var>x</var>
for a Gaussian distribution with standard deviation <var>sigma</var>, using
the formula given above.
</p></blockquote></div>
<pre class="sp">
</pre>
<div class="defun">
— Function: double <b>gsl_ran_gaussian_ziggurat</b> (<var>const gsl_rng * r, double sigma</var>)<var><a name="index-gsl_005fran_005fgaussian_005fziggurat-1581"></a></var><br>
— Function: double <b>gsl_ran_gaussian_ratio_method</b> (<var>const gsl_rng * r, double sigma</var>)<var><a name="index-gsl_005fran_005fgaussian_005fratio_005fmethod-1582"></a></var><br>
<blockquote><p>This function computes a Gaussian random variate using the alternative
Marsaglia-Tsang ziggurat and Kinderman-Monahan-Leva ratio methods. The
Ziggurat algorithm is the fastest available algorithm in most cases.
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_ran_ugaussian</b> (<var>const gsl_rng * r</var>)<var><a name="index-gsl_005fran_005fugaussian-1583"></a></var><br>
— Function: double <b>gsl_ran_ugaussian_pdf</b> (<var>double x</var>)<var><a name="index-gsl_005fran_005fugaussian_005fpdf-1584"></a></var><br>
— Function: double <b>gsl_ran_ugaussian_ratio_method</b> (<var>const gsl_rng * r</var>)<var><a name="index-gsl_005fran_005fugaussian_005fratio_005fmethod-1585"></a></var><br>
<blockquote><p>These functions compute results for the unit Gaussian distribution. They
are equivalent to the functions above with a standard deviation of one,
<var>sigma</var> = 1.
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_cdf_gaussian_P</b> (<var>double x, double sigma</var>)<var><a name="index-gsl_005fcdf_005fgaussian_005fP-1586"></a></var><br>
— Function: double <b>gsl_cdf_gaussian_Q</b> (<var>double x, double sigma</var>)<var><a name="index-gsl_005fcdf_005fgaussian_005fQ-1587"></a></var><br>
— Function: double <b>gsl_cdf_gaussian_Pinv</b> (<var>double P, double sigma</var>)<var><a name="index-gsl_005fcdf_005fgaussian_005fPinv-1588"></a></var><br>
— Function: double <b>gsl_cdf_gaussian_Qinv</b> (<var>double Q, double sigma</var>)<var><a name="index-gsl_005fcdf_005fgaussian_005fQinv-1589"></a></var><br>
<blockquote><p>These functions compute the cumulative distribution functions
P(x), Q(x) and their inverses for the Gaussian
distribution with standard deviation <var>sigma</var>.
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_cdf_ugaussian_P</b> (<var>double x</var>)<var><a name="index-gsl_005fcdf_005fugaussian_005fP-1590"></a></var><br>
— Function: double <b>gsl_cdf_ugaussian_Q</b> (<var>double x</var>)<var><a name="index-gsl_005fcdf_005fugaussian_005fQ-1591"></a></var><br>
— Function: double <b>gsl_cdf_ugaussian_Pinv</b> (<var>double P</var>)<var><a name="index-gsl_005fcdf_005fugaussian_005fPinv-1592"></a></var><br>
— Function: double <b>gsl_cdf_ugaussian_Qinv</b> (<var>double Q</var>)<var><a name="index-gsl_005fcdf_005fugaussian_005fQinv-1593"></a></var><br>
<blockquote><p>These functions compute the cumulative distribution functions
P(x), Q(x) and their inverses for the unit Gaussian
distribution.
</p></blockquote></div>
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