File: The-Gamma-Distribution.html

package info (click to toggle)
gsl-ref-html 2.3-1
  • links: PTS
  • area: non-free
  • in suites: bullseye, buster, sid
  • size: 6,876 kB
  • ctags: 4,574
  • sloc: makefile: 35
file content (120 lines) | stat: -rw-r--r-- 6,466 bytes parent folder | download
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 The GSL Team.

Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled "GNU Free Documentation
License".

(a) The Back-Cover Text is: "You have the freedom to copy and modify this
GNU Manual." -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library &ndash; Reference Manual: The Gamma Distribution</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: The Gamma Distribution">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: The Gamma Distribution">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Function-Index.html#Function-Index" rel="index" title="Function Index">
<link href="Random-Number-Distributions.html#Random-Number-Distributions" rel="up" title="Random Number Distributions">
<link href="The-Flat-_0028Uniform_0029-Distribution.html#The-Flat-_0028Uniform_0029-Distribution" rel="next" title="The Flat (Uniform) Distribution">
<link href="The-Levy-skew-alpha_002dStable-Distribution.html#The-Levy-skew-alpha_002dStable-Distribution" rel="previous" title="The Levy skew alpha-Stable Distribution">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="The-Gamma-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Flat-_0028Uniform_0029-Distribution.html#The-Flat-_0028Uniform_0029-Distribution" accesskey="n" rel="next">The Flat (Uniform) Distribution</a>, Previous: <a href="The-Levy-skew-alpha_002dStable-Distribution.html#The-Levy-skew-alpha_002dStable-Distribution" accesskey="p" rel="previous">The Levy skew alpha-Stable Distribution</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="The-Gamma-Distribution-1"></a>
<h3 class="section">20.15 The Gamma Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fgamma"></a>Function: <em>double</em> <strong>gsl_ran_gamma</strong> <em>(const gsl_rng * <var>r</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><a name="index-Gamma-distribution"></a>
<p>This function returns a random variate from the gamma
distribution.  The distribution function is,
</p>
<div class="example">
<pre class="example">p(x) dx = {1 \over \Gamma(a) b^a} x^{a-1} e^{-x/b} dx
</pre></div>

<p>for <em>x &gt; 0</em>.
</p>
<a name="index-Erlang-distribution"></a>
<p>The gamma distribution with an integer parameter <var>a</var> is known as the Erlang distribution.
</p>
<p>The variates are computed using the Marsaglia-Tsang fast gamma method.
This function for this method was previously called
<code>gsl_ran_gamma_mt</code> and can still be accessed using this name.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fgamma_005fknuth"></a>Function: <em>double</em> <strong>gsl_ran_gamma_knuth</strong> <em>(const gsl_rng * <var>r</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><p>This function returns a gamma variate using the algorithms from Knuth (vol 2).
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fgamma_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_gamma_pdf</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><p>This function computes the probability density <em>p(x)</em> at <var>x</var>
for a gamma distribution with parameters <var>a</var> and <var>b</var>, using the
formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fgamma_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_gamma_P</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgamma_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_gamma_Q</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgamma_005fPinv"></a>Function: <em>double</em> <strong>gsl_cdf_gamma_Pinv</strong> <em>(double <var>P</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgamma_005fQinv"></a>Function: <em>double</em> <strong>gsl_cdf_gamma_Qinv</strong> <em>(double <var>Q</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(x)</em>, <em>Q(x)</em> and their inverses for the gamma
distribution with parameters <var>a</var> and <var>b</var>.
</p></dd></dl>




</body>
</html>