ceph/src/boost/libs/random/doc/distributions.qbk

   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 ]