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<title>The Gaussian Tail Distribution - GNU Scientific Library -- Reference Manual</title>
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<a name="The-Gaussian-Tail-Distribution"></a>
Next: <a rel="next" accesskey="n" href="The-Bivariate-Gaussian-Distribution.html">The Bivariate Gaussian Distribution</a>,
Previous: <a rel="previous" accesskey="p" href="The-Gaussian-Distribution.html">The Gaussian Distribution</a>,
Up: <a rel="up" accesskey="u" href="Random-Number-Distributions.html">Random Number Distributions</a>
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<h3 class="section">19.3 The Gaussian Tail Distribution</h3>
<div class="defun">
— Function: double <b>gsl_ran_gaussian_tail</b> (<var>const gsl_rng * r, double a, double sigma</var>)<var><a name="index-gsl_005fran_005fgaussian_005ftail-1594"></a></var><br>
<blockquote><p><a name="index-Gaussian-Tail-distribution-1595"></a>This function provides random variates from the upper tail of a Gaussian
distribution with standard deviation <var>sigma</var>. The values returned
are larger than the lower limit <var>a</var>, which must be positive. The
method is based on Marsaglia's famous rectangle-wedge-tail algorithm (Ann.
Math. Stat. 32, 894–899 (1961)), with this aspect explained in Knuth, v2,
3rd ed, p139,586 (exercise 11).
<p>The probability distribution for Gaussian tail random variates is,
<pre class="example"> p(x) dx = {1 \over N(a;\sigma) \sqrt{2 \pi \sigma^2}} \exp (- x^2/(2 \sigma^2)) dx
</pre>
<p class="noindent">for x > a where N(a;\sigma) is the normalization constant,
<pre class="example"> N(a;\sigma) = (1/2) erfc(a / sqrt(2 sigma^2)).
</pre>
</blockquote></div>
<div class="defun">
— Function: double <b>gsl_ran_gaussian_tail_pdf</b> (<var>double x, double a, double sigma</var>)<var><a name="index-gsl_005fran_005fgaussian_005ftail_005fpdf-1596"></a></var><br>
<blockquote><p>This function computes the probability density p(x) at <var>x</var>
for a Gaussian tail distribution with standard deviation <var>sigma</var> and
lower limit <var>a</var>, using the formula given above.
</p></blockquote></div>
<pre class="sp">
</pre>
<div class="defun">
— Function: double <b>gsl_ran_ugaussian_tail</b> (<var>const gsl_rng * r, double a</var>)<var><a name="index-gsl_005fran_005fugaussian_005ftail-1597"></a></var><br>
— Function: double <b>gsl_ran_ugaussian_tail_pdf</b> (<var>double x, double a</var>)<var><a name="index-gsl_005fran_005fugaussian_005ftail_005fpdf-1598"></a></var><br>
<blockquote><p>These functions compute results for the tail of a unit Gaussian
distribution. They are equivalent to the functions above with a standard
deviation of one, <var>sigma</var> = 1.
</p></blockquote></div>
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