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 9In addition to the [link boost_random.reference.generators random number generators], 10this library provides distribution functions which map one distribution 11(often a uniform distribution provided by some generator) to another. 12 13Usually, there are several possible implementations of any given mapping. 14Often, there is a choice between using more space, more invocations of the 15underlying source of random numbers, or more time-consuming arithmetic such 16as trigonometric functions. This interface description does not mandate any 17specific implementation. However, implementations which cannot reach certain 18values of the specified distribution or otherwise do not converge 19statistically 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] 111