File: The-Binomial-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 (108 lines) | stat: -rw-r--r-- 5,473 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
<!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 Binomial Distribution</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: The Binomial Distribution">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: The Binomial 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-Multinomial-Distribution.html#The-Multinomial-Distribution" rel="next" title="The Multinomial Distribution">
<link href="The-Bernoulli-Distribution.html#The-Bernoulli-Distribution" rel="previous" title="The Bernoulli 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-Binomial-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Multinomial-Distribution.html#The-Multinomial-Distribution" accesskey="n" rel="next">The Multinomial Distribution</a>, Previous: <a href="The-Bernoulli-Distribution.html#The-Bernoulli-Distribution" accesskey="p" rel="previous">The Bernoulli 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-Binomial-Distribution-1"></a>
<h3 class="section">20.32 The Binomial Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fbinomial"></a>Function: <em>unsigned int</em> <strong>gsl_ran_binomial</strong> <em>(const gsl_rng * <var>r</var>, double <var>p</var>, unsigned int <var>n</var>)</em></dt>
<dd><a name="index-Binomial-random-variates"></a>
<p>This function returns a random integer from the binomial distribution,
the number of successes in <var>n</var> independent trials with probability
<var>p</var>.  The probability distribution for binomial variates is,
</p>
<div class="example">
<pre class="example">p(k) = {n! \over k! (n-k)! } p^k (1-p)^{n-k}
</pre></div>

<p>for <em>0 &lt;= k &lt;= n</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fbinomial_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_binomial_pdf</strong> <em>(unsigned int <var>k</var>, double <var>p</var>, unsigned int <var>n</var>)</em></dt>
<dd><p>This function computes the probability <em>p(k)</em> of obtaining <var>k</var>
from a binomial distribution with parameters <var>p</var> and <var>n</var>, using
the formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fbinomial_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_binomial_P</strong> <em>(unsigned int <var>k</var>, double <var>p</var>, unsigned int <var>n</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fbinomial_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_binomial_Q</strong> <em>(unsigned int <var>k</var>, double <var>p</var>, unsigned int <var>n</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(k)</em>, <em>Q(k)</em>  for the binomial
distribution with parameters <var>p</var> and <var>n</var>.
</p></dd></dl>





</body>
</html>