breeze.stats.distributions

Type members

Classlikes

case class AliasTable[I](probs: DenseVector[Double], aliases: DenseVector[Int], outcomes: IndexedSeq[I], rand: RandBasis)
case class Bernoulli(p: Double)(implicit rand: RandBasis) extends DiscreteDistr[Boolean] with Moments[Double, Double]

A Bernoulli distribution represents a distribution over weighted coin flips

A Bernoulli distribution represents a distribution over weighted coin flips

Value Params
p

the probability of true

Companion
object
object Bernoulli extends ExponentialFamily[Bernoulli, Boolean] with HasConjugatePrior[Bernoulli, Boolean]
Companion
class
case class Beta(a: Double, b: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf with HasInverseCdf

The Beta distribution, which is the conjugate prior for the Bernoulli distribution

The Beta distribution, which is the conjugate prior for the Bernoulli distribution

Value Params
a

the number of pseudo-observations for true

b

the number of pseudo-observations for false

Companion
object
object Beta extends ExponentialFamily[Beta, Double] with ContinuousDistributionUFuncProvider[Double, Beta]
Companion
class
case class Binomial(n: Int, p: Double)(implicit rand: RandBasis) extends DiscreteDistr[Int] with Moments[Double, Double]

A binomial distribution returns how many coin flips out of n are heads, where numYes is the probability of any one coin being heads.

A binomial distribution returns how many coin flips out of n are heads, where numYes is the probability of any one coin being heads.

Value Params
n

is the number of coin flips

p

the probability of any one being true

case class CauchyDistribution(median: Double, scale: Double)(implicit rand: RandBasis) extends ApacheContinuousDistribution

The Cauchy-distribution

The Cauchy-distribution

Companion
object
case class ChiSquared(k: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf with HasInverseCdf

Chi-Squared distribution with k degrees of freedom.

Chi-Squared distribution with k degrees of freedom.

Companion
object
trait ContinuousDistr[T] extends Density[T] with Rand[T]

Represents a continuous Distribution. Why T? just in case.

Represents a continuous Distribution. Why T? just in case.

trait Density[T]

Represents an unnormalized probability distribution.

Represents an unnormalized probability distribution.

case class Dirichlet[T, @specialized(Int) I](params: T)(implicit space: EnumeratedCoordinateField[T, I, Double], rand: RandBasis) extends ContinuousDistr[T]

Represents a Dirichlet distribution, the conjugate prior to the multinomial.

Represents a Dirichlet distribution, the conjugate prior to the multinomial.

Companion
object
object Dirichlet

Provides several defaults for Dirichlets, one for Arrays and one for Counters.

Provides several defaults for Dirichlets, one for Arrays and one for Counters.

Companion
class
trait DiscreteDistr[T] extends Density[T] with Rand[T]

Represents a discrete Distribution.

Represents a discrete Distribution.

case class Exponential(rate: Double)(implicit basis: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf with HasInverseCdf
Companion
object
trait ExponentialFamily[D, T]
case class FDistribution(numeratorDegreesOfFreedom: Double, denominatorDegreesOfFreedom: Double) extends ApacheContinuousDistribution

The F-distribution - ratio of two scaled chi^2 variables

The F-distribution - ratio of two scaled chi^2 variables

Companion
object
case class Gamma(shape: Double, scale: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf with HasInverseCdf

Represents a Gamma distribution. E[X] = shape * scale

Represents a Gamma distribution. E[X] = shape * scale

Companion
object
Companion
class
case class Gaussian(mu: Double, sigma: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf with HasInverseCdf

Represents a Gaussian distribution over a single real variable.

Represents a Gaussian distribution over a single real variable.

Companion
object
case class Geometric(p: Double)(implicit rand: RandBasis) extends DiscreteDistr[Int] with Moments[Double, Double]

The Geometric distribution calculates the number of trials until the first success, which happens with probability p.

The Geometric distribution calculates the number of trials until the first success, which happens with probability p.

Companion
object
Companion
class
case class Gumbel(location: Double, scale: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf
trait HasCdf
trait HasConjugatePrior[Likelihood <: Density[T], T] extends ExponentialFamily[Likelihood, T]

Trait representing conjugate priors. See Dirichlet for an example.

Trait representing conjugate priors. See Dirichlet for an example.

class HypergeometricDistribution(populationSize: Int, numberOfSuccesses: Int, sampleSize: Int) extends ApacheDiscreteDistribution

The Hypergeometric-distribution - ratio of two scaled chi^2 variables

The Hypergeometric-distribution - ratio of two scaled chi^2 variables

Companion
object
case class InvGamma(shape: Double, scale: Double)(implicit basis: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf
case class InvWishart(df: Int, scale: DenseMatrix[Double])(implicit rand: RandBasis) extends ContinuousDistr[DenseMatrix[Double]] with Moments[DenseMatrix[Double], DenseMatrix[Double]]
case class Laplace(location: Double, scale: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf

http://en.wikipedia.org/wiki/Laplace_distribution

case class LevyDistribution(mu: Double, c: Double, generator: RandomGenerator) extends ApacheContinuousDistribution

The Levy-distribution - ratio of two scaled chi^2 variables

The Levy-distribution - ratio of two scaled chi^2 variables

Companion
object
case class LogNormal(mu: Double, sigma: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf with HasInverseCdf

A log normal distribution is distributed such that log X ~ Normal(\mu, \sigma)

A log normal distribution is distributed such that log X ~ Normal(\mu, \sigma)

Companion
object
case class Logarthmic(p: Double)(implicit rand: RandBasis) extends DiscreteDistr[Int] with Moments[Double, Double]

The Logarithmic distribution

trait Moments[Mean, Variance]

Interface for distributions that can report on some of their moments

Interface for distributions that can report on some of their moments

case class Multinomial[T, I](params: T)(implicit ev: ConversionOrSubtype[T, QuasiTensor[I, Double]], sumImpl: Impl[T, Double], rand: RandBasis) extends DiscreteDistr[I]

Represents a Multinomial distribution over elements. You can make a distribution over any breeze.linalg.QuasiTensor, which includes DenseVectors and Counters.

Represents a Multinomial distribution over elements. You can make a distribution over any breeze.linalg.QuasiTensor, which includes DenseVectors and Counters.

TODO: I should probably rename this to Discrete or something, since it only handles one draw.

Companion
object
object Multinomial

Provides routines to create Multinomials

Provides routines to create Multinomials

Companion
class
case class MultivariateGaussian(mean: DenseVector[Double], covariance: DenseMatrix[Double])(implicit rand: RandBasis) extends ContinuousDistr[DenseVector[Double]] with Moments[DenseVector[Double], DenseMatrix[Double]]

Represents a Gaussian distribution over a single real variable.

Represents a Gaussian distribution over a single real variable.

case class NegativeBinomial(r: Double, p: Double)(implicit rand: RandBasis) extends DiscreteDistr[Int]

Negative Binomial Distribution

Negative Binomial Distribution

Value Params
p

prob of success

r

number of failures until stop

case class Pareto(scale: Double, shape: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf

http://en.wikipedia.org/wiki/Laplace_distribution

trait PdfIsUFunc[U <: UFunc, T, P <: PdfIsUFunc[U, T, P]]
case class Poisson(mean: Double)(implicit rand: RandBasis) extends DiscreteDistr[Int] with Moments[Double, Double]

Represents a Poisson random variable.

Represents a Poisson random variable.

Companion
object
object Poisson extends ExponentialFamily[Poisson, Int]
Companion
class
class Polya[T, @specialized(Int) I](params: T)(implicit space: MutableEnumeratedCoordinateField[T, I, Double], rand: RandBasis) extends DiscreteDistr[I]

Represents a Polya distribution, a.k.a Dirichlet compound Multinomial distribution see http://en.wikipedia.org/wiki/Multivariate_Polya_distribution

Represents a Polya distribution, a.k.a Dirichlet compound Multinomial distribution see http://en.wikipedia.org/wiki/Multivariate_Polya_distribution

Companion
object
object Polya
Companion
class
trait Process[T] extends Rand[T]

A Rand that changes based on previous draws.

A Rand that changes based on previous draws.

trait Rand[@specialized(Int, Double) +T] extends Serializable

A trait for monadic distributions. Provides support for use in for-comprehensions

A trait for monadic distributions. Provides support for use in for-comprehensions

Companion
object
object Rand extends RandBasis

Provides a number of random generators, with random seed set to some function of system time and identity hashcode of some object

Provides a number of random generators, with random seed set to some function of system time and identity hashcode of some object

Companion
class
class RandBasis(val generator: RandomGenerator) extends Serializable

Provides standard combinators and such to use to compose new Rands.

Provides standard combinators and such to use to compose new Rands.

Companion
object
object RandBasis
Companion
class
case class Rayleigh(scale: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf
case class StudentsT(degreesOfFreedom: Double)(implicit randBasis: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf
Companion
object
@SerialVersionUID(1L)
class ThreadLocalRandomGenerator(genThunk: => RandomGenerator) extends RandomGenerator with Serializable

An Apache-compatible RandomGenerator that creates a new RandomGenerator per thread. The thunk should be thread-safe, using atomics or something.

An Apache-compatible RandomGenerator that creates a new RandomGenerator per thread. The thunk should be thread-safe, using atomics or something.

class TriangularDistribution(a: Double, c: Double, b: Double) extends ApacheContinuousDistribution with Moments[Double, Double]

The Triangular-distribution - ratio of two scaled chi^2 variables

The Triangular-distribution - ratio of two scaled chi^2 variables

Companion
object
case class Uniform(low: Double, high: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double] with HasCdf with HasInverseCdf
Companion
object
Companion
class
class VariableKernelEmpiricalDistribution(data: Array[Double], binCount: Int) extends ApacheContinuousDistribution

The Weibull-distribution - ratio of two scaled chi^2 variables

The Weibull-distribution - ratio of two scaled chi^2 variables

Companion
object
case class VonMises(mu: Double, k: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double]

Represents a Von Mises distribution, which is a distribution over angles.

Represents a Von Mises distribution, which is a distribution over angles.

Value Params
k

is the concentration, which is like 1/gaussian variance

mu

is the mean of the distribution, ~ gaussian mean

Companion
object
object VonMises extends ExponentialFamily[VonMises, Double]
Companion
class
case class Wald(mean: Double, shape: Double)(implicit rand: RandBasis) extends ContinuousDistr[Double] with Moments[Double, Double]

Also known as the inverse Gaussian Distribution

Also known as the inverse Gaussian Distribution

http://en.wikipedia.org/wiki/Inverse_Gaussian_distribution

case class WeibullDistribution(alpha: Double, beta: Double) extends ApacheContinuousDistribution

The Weibull-distribution - ratio of two scaled chi^2 variables

The Weibull-distribution - ratio of two scaled chi^2 variables

Companion
object
case class Wishart(df: Int, scale: DenseMatrix[Double])(implicit randBasis: RandBasis) extends ContinuousDistr[DenseMatrix[Double]] with Moments[DenseMatrix[Double], DenseMatrix[Double]]
case class ZipfDistribution(numberOfElements: Int, exponent: Double) extends ApacheDiscreteDistribution