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- [/
- / Copyright (c) 2009 Steven Watanabe
- /
- / Distributed under the Boost Software License, Version 1.0. (See
- / accompanying file LICENSE_1_0.txt or copy at
- / http://www.boost.org/LICENSE_1_0.txt)
- ]
- In addition to the [link boost_random.reference.generators random number generators],
- this library provides distribution functions which map one distribution
- (often a uniform distribution provided by some generator) to another.
- Usually, there are several possible implementations of any given mapping.
- Often, there is a choice between using more space, more invocations of the
- underlying source of random numbers, or more time-consuming arithmetic such
- as trigonometric functions. This interface description does not mandate any
- specific implementation. However, implementations which cannot reach certain
- values of the specified distribution or otherwise do not converge
- statistically to it are not acceptable.
- [table Uniform Distributions
- [[distribution] [explanation] [example]]
- [[__uniform_smallint] [discrete uniform distribution on a small set of integers
- (much smaller than the range of the underlying
- generator)]
- [drawing from an urn]]
- [[__uniform_int_distribution] [discrete uniform distribution on a set of integers; the
- underlying generator may be called several times to gather
- enough randomness for the output]
- [drawing from an urn]]
- [[__uniform_01] [continuous uniform distribution on the range [0,1);
- important basis for other distributions]
- [-]]
- [[__uniform_real_distribution] [continuous uniform distribution on some range [min, max) of
- real numbers]
- [for the range [0, 2pi): randomly dropping a stick and
- measuring its angle in radians (assuming the angle is
- uniformly distributed)]]
- ]
- [table Bernoulli Distributions
- [[distribution] [explanation] [example]]
- [[__bernoulli_distribution] [Bernoulli experiment: discrete boolean valued
- distribution with configurable probability]
- [tossing a coin (p=0.5)]]
- [[__binomial_distribution] [counts outcomes of repeated Bernoulli
- experiments]
- [tossing a coin 20 times and counting how many
- front sides are shown]]
- [[__geometric_distribution] [measures distance between outcomes of repeated
- Bernoulli experiments]
- [throwing a die several times and counting the
- number of tries until a "6" appears for the
- first time]]
- [[__negative_binomial_distribution] [Counts the number of failures of repeated
- Bernoulli experiments required to get some constant
- number of successes.]
- [flipping a coin and counting the number of
- heads that show up before we get 3 tails]]
- ]
- [table Poisson Distributions
- [[distribution] [explanation] [example]]
- [[__poisson_distribution][poisson distribution]
- [counting the number of alpha particles emitted
- by radioactive matter in a fixed period of time]]
- [[__exponential_distribution] [exponential distribution]
- [measuring the inter-arrival time of alpha
- particles emitted by radioactive matter]]
- [[__gamma_distribution][gamma distribution][-]]
- [[__hyperexponential_distribution] [hyperexponential distribution] [service time of k-parallel servers each with a given service rate and probability to be chosen]]
- [[__weibull_distribution] [weibull distribution] [-]]
- [[__extreme_value_distribution] [extreme value distribution] [-]]
- [[__beta_distribution] [beta distribution] [-]]
- [[__laplace_distribution] [laplace distribution] [-]]
- ]
- [table Normal Distributions
- [[distribution] [explanation] [example]]
- [[__normal_distribution] [counts outcomes of (infinitely) repeated Bernoulli
- experiments]
- [tossing a coin 10000 times and counting how many
- front sides are shown]]
- [[__lognormal_distribution] [lognormal distribution (sometimes used in
- simulations)]
- [measuring the job completion time of an assembly
- line worker]]
- [[__chi_squared_distribution][chi-squared distribution][-]]
- [[__non_central_chi_squared_distribution][non-central chi-squared distribution][-]]
- [[__cauchy_distribution][Cauchy distribution][-]]
- [[__fisher_f_distribution][Fisher F distribution][-]]
- [[__student_t_distribution][Student t distribution][-]]
- ]
- [table Sampling Distributions
- [[distribution] [explanation] [example]]
- [[__discrete_distribution][discrete distribution with specific probabilities][rolling an unfair die]]
- [[__piecewise_constant_distribution][-][-]]
- [[__piecewise_linear_distribution][-][-]]
- ]
- [table Miscellaneous Distributions
- [[distribution] [explanation] [example]]
- [[__triangle_distribution] [triangle distribution] [-]]
- [[__uniform_on_sphere] [uniform distribution on a unit sphere of arbitrary
- dimension]
- [choosing a random point on Earth (assumed to be a
- sphere) where to spend the next vacations]]
- ]
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