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1 | [/ |
2 | / Copyright (c) 2009 Steven Watanabe | |
3 | / | |
4 | / Distributed under the Boost Software License, Version 1.0. (See | |
5 | / accompanying file LICENSE_1_0.txt or copy at | |
6 | / http://www.boost.org/LICENSE_1_0.txt) | |
7 | ] | |
8 | ||
9 | In addition to the [link boost_random.reference.generators random number generators], | |
10 | this library provides distribution functions which map one distribution | |
11 | (often a uniform distribution provided by some generator) to another. | |
12 | ||
13 | Usually, there are several possible implementations of any given mapping. | |
14 | Often, there is a choice between using more space, more invocations of the | |
15 | underlying source of random numbers, or more time-consuming arithmetic such | |
16 | as trigonometric functions. This interface description does not mandate any | |
17 | specific implementation. However, implementations which cannot reach certain | |
18 | values of the specified distribution or otherwise do not converge | |
19 | statistically to it are not acceptable. | |
20 | ||
21 | [table Uniform Distributions | |
22 | [[distribution] [explanation] [example]] | |
23 | [[__uniform_smallint] [discrete uniform distribution on a small set of integers | |
24 | (much smaller than the range of the underlying | |
25 | generator)] | |
26 | [drawing from an urn]] | |
27 | [[__uniform_int_distribution] [discrete uniform distribution on a set of integers; the | |
28 | underlying generator may be called several times to gather | |
29 | enough randomness for the output] | |
30 | [drawing from an urn]] | |
31 | [[__uniform_01] [continuous uniform distribution on the range [0,1); | |
32 | important basis for other distributions] | |
33 | [-]] | |
34 | [[__uniform_real_distribution] [continuous uniform distribution on some range [min, max) of | |
35 | real numbers] | |
36 | [for the range [0, 2pi): randomly dropping a stick and | |
37 | measuring its angle in radians (assuming the angle is | |
38 | uniformly distributed)]] | |
39 | ] | |
40 | ||
41 | [table Bernoulli Distributions | |
42 | [[distribution] [explanation] [example]] | |
43 | [[__bernoulli_distribution] [Bernoulli experiment: discrete boolean valued | |
44 | distribution with configurable probability] | |
45 | [tossing a coin (p=0.5)]] | |
46 | [[__binomial_distribution] [counts outcomes of repeated Bernoulli | |
47 | experiments] | |
48 | [tossing a coin 20 times and counting how many | |
49 | front sides are shown]] | |
50 | [[__geometric_distribution] [measures distance between outcomes of repeated | |
51 | Bernoulli experiments] | |
52 | [throwing a die several times and counting the | |
53 | number of tries until a "6" appears for the | |
54 | first time]] | |
55 | [[__negative_binomial_distribution] [Counts the number of failures of repeated | |
56 | Bernoulli experiments required to get some constant | |
57 | number of successes.] | |
58 | [flipping a coin and counting the number of | |
59 | heads that show up before we get 3 tails]] | |
60 | ] | |
61 | ||
62 | [table Poisson Distributions | |
63 | [[distribution] [explanation] [example]] | |
64 | [[__poisson_distribution][poisson distribution] | |
65 | [counting the number of alpha particles emitted | |
66 | by radioactive matter in a fixed period of time]] | |
67 | [[__exponential_distribution] [exponential distribution] | |
68 | [measuring the inter-arrival time of alpha | |
69 | particles emitted by radioactive matter]] | |
70 | [[__gamma_distribution][gamma distribution][-]] | |
71 | [[__hyperexponential_distribution] [hyperexponential distribution] [service time of k-parallel servers each with a given service rate and probability to be chosen]] | |
72 | [[__weibull_distribution] [weibull distribution] [-]] | |
73 | [[__extreme_value_distribution] [extreme value distribution] [-]] | |
74 | [[__beta_distribution] [beta distribution] [-]] | |
75 | [[__laplace_distribution] [laplace distribution] [-]] | |
76 | ] | |
77 | ||
78 | [table Normal Distributions | |
79 | [[distribution] [explanation] [example]] | |
80 | [[__normal_distribution] [counts outcomes of (infinitely) repeated Bernoulli | |
81 | experiments] | |
82 | [tossing a coin 10000 times and counting how many | |
83 | front sides are shown]] | |
84 | [[__lognormal_distribution] [lognormal distribution (sometimes used in | |
85 | simulations)] | |
86 | [measuring the job completion time of an assembly | |
87 | line worker]] | |
88 | [[__chi_squared_distribution][chi-squared distribution][-]] | |
89 | [[__non_central_chi_squared_distribution][non-central chi-squared distribution][-]] | |
90 | [[__cauchy_distribution][Cauchy distribution][-]] | |
91 | [[__fisher_f_distribution][Fisher F distribution][-]] | |
92 | [[__student_t_distribution][Student t distribution][-]] | |
93 | ] | |
94 | ||
95 | [table Sampling Distributions | |
96 | [[distribution] [explanation] [example]] | |
97 | [[__discrete_distribution][discrete distribution with specific probabilities][rolling an unfair die]] | |
98 | [[__piecewise_constant_distribution][-][-]] | |
99 | [[__piecewise_linear_distribution][-][-]] | |
100 | ] | |
101 | ||
102 | ||
103 | [table Miscellaneous Distributions | |
104 | [[distribution] [explanation] [example]] | |
105 | [[__triangle_distribution] [triangle distribution] [-]] | |
106 | [[__uniform_on_sphere] [uniform distribution on a unit sphere of arbitrary | |
107 | dimension] | |
108 | [choosing a random point on Earth (assumed to be a | |
109 | sphere) where to spend the next vacations]] | |
110 | ] |