dist

package
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 Go to latest Published: Nov 6, 2026 License: AGPL-3.0 Imports: 8 Imported by: 0

Documentation

Overview

Package dist holds the distribution families and their exact samplers. Every family implements Distribution; continuous families also implement Quantiler and discrete families PMFer. Simulation code never calls Fill directly: it draws through a Sampler.

Index

Examples

Constants

View Source 
const (

	// DefaultPERTShape is the t of the modified PERT when none is given.
	DefaultPERTShape = 4
)

Variables

This section is empty.

Functions

func PoissonCount 

func PoissonCount(r *rand.Rand, lambda float64) uint64

PoissonCount draws one count for a rate that changes on every call, such as a mixed-Poisson rate drawn per period. The PTRS constants are built inline: a square root and a logarithm per call.

Types

type Bernoulli 

type Bernoulli struct {
	// contains filtered or unexported fields
}

Bernoulli is a single trial with success probability p.

func NewBernoulli 

func NewBernoulli(p float64) (Bernoulli, error)

NewBernoulli validates 0 ≤ p ≤ 1.

func (Bernoulli) CDF 

func (d Bernoulli) CDF(x float64) float64

func (Bernoulli) Fill 

func (d Bernoulli) Fill(r *rand.Rand, dst []float64)

func (Bernoulli) Laplace 

func (Bernoulli) Laplace(complex128) (complex128, bool)

func (Bernoulli) Mean 

func (d Bernoulli) Mean() float64

func (Bernoulli) Nodes 

func (Bernoulli) Nodes(_, _ []float64) bool

func (Bernoulli) PMF 

func (d Bernoulli) PMF(x float64) float64

func (Bernoulli) Quantile 

func (d Bernoulli) Quantile(p float64) float64

func (Bernoulli) QuantileUpper 

func (d Bernoulli) QuantileUpper(q float64) float64

func (Bernoulli) Support 

func (d Bernoulli) Support() (lo, hi float64)

func (Bernoulli) Survival 

func (d Bernoulli) Survival(x float64) float64

func (Bernoulli) Var 

func (d Bernoulli) Var() float64

type Beta 

type Beta struct {
	// contains filtered or unexported fields
}

Beta is the Beta distribution on [0, 1], drawn as X/(X+Y) from two Gammas.

func NewBeta 

func NewBeta(alpha, beta float64) (Beta, error)

NewBeta validates alpha > 0 and beta > 0.

func NewBetaFromMeanSD 

func NewBetaFromMeanSD(mean, sd float64) (Beta, error)

NewBetaFromMeanSD converts a mean and standard deviation; it fails when no Beta has them, that is when sd² ≥ mean·(1 − mean).

func (Beta) CDF 

func (d Beta) CDF(x float64) float64

func (Beta) Fill 

func (d Beta) Fill(r *rand.Rand, dst []float64)

func (Beta) Laplace 

func (Beta) Laplace(complex128) (complex128, bool)

func (Beta) Mean 

func (d Beta) Mean() float64

func (Beta) Nodes 

func (d Beta) Nodes(x, w []float64) bool

func (Beta) Quantile 

func (d Beta) Quantile(p float64) float64

Quantile inverts the regularised incomplete beta function to full precision, seeded by gonum's inverse or by the small-x series I_x(a, b) ≈ x^a / (a·B(a, b)) when that seed is 0.

func (Beta) QuantileUpper 

func (d Beta) QuantileUpper(q float64) float64

QuantileUpper inverts the survival function the same way; the seed uses the mirrored inverse.

func (Beta) Support 

func (d Beta) Support() (lo, hi float64)

func (Beta) Survival 

func (d Beta) Survival(x float64) float64

func (Beta) Var 

func (d Beta) Var() float64

type Binomial 

type Binomial struct {
	// contains filtered or unexported fields
}

Binomial counts successes in n trials with probability p.

func NewBinomial 

func NewBinomial(n, p float64) (Binomial, error)

NewBinomial validates n ≥ 0 integer and 0 ≤ p ≤ 1.

func (Binomial) CDF 

func (d Binomial) CDF(x float64) float64

func (Binomial) Fill 

func (d Binomial) Fill(r *rand.Rand, dst []float64)

func (Binomial) Laplace 

func (Binomial) Laplace(complex128) (complex128, bool)

func (Binomial) Mean 

func (d Binomial) Mean() float64

func (Binomial) Nodes 

func (Binomial) Nodes(_, _ []float64) bool

func (Binomial) PMF 

func (d Binomial) PMF(x float64) float64

func (Binomial) Quantile 

func (d Binomial) Quantile(p float64) float64

func (Binomial) QuantileUpper 

func (d Binomial) QuantileUpper(q float64) float64

QuantileUpper is the smallest k with Survival(k) ≤ q.

func (Binomial) Support 

func (d Binomial) Support() (lo, hi float64)

func (Binomial) Survival 

func (d Binomial) Survival(x float64) float64

func (Binomial) Var 

func (d Binomial) Var() float64

type Capped 

type Capped struct {
	// contains filtered or unexported fields
}

Capped is min(X, c): the distribution of X with its upper tail collapsed into an atom at c. Draws cost the same as X.

func NewCapped 

func NewCapped(d Continuous, c float64) (Capped, error)

NewCapped validates that c lies inside the support and computes the moments from the partial expectations below c and the atom at c.

func (Capped) Atom 

func (d Capped) Atom() float64

Atom is the probability mass at the cap.

func (Capped) CDF 

func (d Capped) CDF(x float64) float64

func (Capped) Fill 

func (d Capped) Fill(r *rand.Rand, dst []float64)

func (Capped) Laplace 

func (Capped) Laplace(complex128) (complex128, bool)

func (Capped) Mean 

func (d Capped) Mean() float64

func (Capped) Nodes 

func (Capped) Nodes(_, _ []float64) bool

func (Capped) Quantile 

func (d Capped) Quantile(p float64) float64

func (Capped) QuantileUpper 

func (d Capped) QuantileUpper(q float64) float64

func (Capped) Support 

func (d Capped) Support() (lo, hi float64)

func (Capped) Survival 

func (d Capped) Survival(x float64) float64

func (Capped) Var 

func (d Capped) Var() float64

type Categorical 

type Categorical struct {
	// contains filtered or unexported fields
}

Categorical draws from a finite set of values with given probabilities, by Vose's alias method in O(1) per draw. Values may repeat.

func NewCategorical 

func NewCategorical(values, probs []float64) (Categorical, error)

NewCategorical validates the lengths match, values are finite, probabilities are non-negative and sum to 1 within 1e-12.

func NewEmpirical 

func NewEmpirical(values []float64) (Categorical, error)

NewEmpirical is a Categorical with equal weights: resampling of observed data.

func (Categorical) CDF 

func (d Categorical) CDF(x float64) float64

func (Categorical) Fill 

func (d Categorical) Fill(r *rand.Rand, dst []float64)

func (Categorical) Laplace 

func (d Categorical) Laplace(s complex128) (complex128, bool)

Categorical: the exact finite mixture.

func (Categorical) Len 

func (d Categorical) Len() int

Len returns the number of entries.

func (Categorical) Mean 

func (d Categorical) Mean() float64

func (Categorical) Nodes 

func (d Categorical) Nodes(x, w []float64) bool

Nodes of a Categorical are its atoms, exact for every g, when they fit.

func (Categorical) PMF 

func (d Categorical) PMF(x float64) float64

func (Categorical) Quantile 

func (d Categorical) Quantile(p float64) float64

Quantile is the smallest value with at least a fraction p of the mass at or below it.

func (Categorical) QuantileUpper 

func (d Categorical) QuantileUpper(q float64) float64

QuantileUpper is the smallest value with at most q of the mass above it.

func (Categorical) Support 

func (d Categorical) Support() (lo, hi float64)

func (Categorical) Survival 

func (d Categorical) Survival(x float64) float64

Survival is P(X > x).

func (Categorical) Var 

func (d Categorical) Var() float64

type Constant 

type Constant struct {
	// contains filtered or unexported fields
}

Constant is a point mass.

func NewConstant 

func NewConstant(c float64) (Constant, error)

NewConstant validates that the value is finite.

func (Constant) CDF 

func (d Constant) CDF(x float64) float64

func (Constant) Fill 

func (d Constant) Fill(_ *rand.Rand, dst []float64)

func (Constant) Laplace 

func (d Constant) Laplace(s complex128) (complex128, bool)

func (Constant) Mean 

func (d Constant) Mean() float64

func (Constant) Nodes 

func (d Constant) Nodes(x, w []float64) bool

func (Constant) Quantile 

func (d Constant) Quantile(float64) float64

func (Constant) QuantileUpper 

func (d Constant) QuantileUpper(float64) float64

func (Constant) Support 

func (d Constant) Support() (lo, hi float64)

func (Constant) Survival 

func (d Constant) Survival(x float64) float64

func (Constant) Var 

func (d Constant) Var() float64

type Continuous 

type Continuous interface {
	Distribution
	Quantiler
}

Continuous is a distribution with the tail-safe inverses the wrappers need.

type Distribution 

type Distribution interface {
	Fill(r *rand.Rand, dst []float64)
	Mean() float64
	Var() float64
	Support() (lo, hi float64)
	CDF(x float64) float64
	Laplace(s complex128) (value complex128, ok bool)
	Nodes(x, w []float64) bool
	Quantiler
}

Distribution is one family with fixed parameters. Fill writes len(dst) independent draws and never allocates. Laplace is E[exp(−s·X)] for complex s with Re(s) ≥ 0 in closed form; ok is false for a family without one, and the caller integrates numerically instead. Nodes fills a Gauss rule for the family's own density (see nodes.go); false for a family without one.

Example

Fill draws straight from a distribution when no Sampler is wanted. 

package main

import (
	"fmt"
	"math/rand/v2"

	"code.eitanity.com/variate/dist"
)

func main() {
	d, _ := dist.NewExponential(2)
	r := rand.New(rand.NewPCG(1, 2))
	buf := make([]float64, 4)
	d.Fill(r, buf)
	fmt.Println(len(buf), buf[0] > 0)
}

Output:
4 true

type Exponential 

type Exponential struct {
	// contains filtered or unexported fields
}

Exponential has the given mean.

func NewExponential 

func NewExponential(mean float64) (Exponential, error)

NewExponential validates mean > 0.

func NewExponentialFromRate 

func NewExponentialFromRate(rate float64) (Exponential, error)

NewExponentialFromRate converts a rate.

func (Exponential) CDF 

func (d Exponential) CDF(x float64) float64

func (Exponential) Fill 

func (d Exponential) Fill(r *rand.Rand, dst []float64)

func (Exponential) Laplace 

func (d Exponential) Laplace(s complex128) (complex128, bool)

func (Exponential) Mean 

func (d Exponential) Mean() float64

func (Exponential) Nodes 

func (Exponential) Nodes(_, _ []float64) bool

func (Exponential) Quantile 

func (d Exponential) Quantile(p float64) float64

func (Exponential) QuantileUpper 

func (d Exponential) QuantileUpper(q float64) float64

func (Exponential) Support 

func (d Exponential) Support() (lo, hi float64)

func (Exponential) Survival 

func (d Exponential) Survival(x float64) float64

func (Exponential) Var 

func (d Exponential) Var() float64

type GPD 

type GPD struct {
	// contains filtered or unexported fields
}

GPD is the generalised Pareto with location mu, scale sigma and shape xi. Shape 0 is the exponential; a negative shape bounds the support above.

func NewGPD 

func NewGPD(mu, sigma, xi float64) (GPD, error)

NewGPD validates sigma > 0 and finite mu and xi.

func (GPD) CDF 

func (d GPD) CDF(x float64) float64

func (GPD) Fill 

func (d GPD) Fill(r *rand.Rand, dst []float64)

func (GPD) Laplace 

func (GPD) Laplace(complex128) (complex128, bool)

func (GPD) Mean 

func (d GPD) Mean() float64

Mean is +Inf for xi ≥ 1.

func (GPD) Nodes 

func (GPD) Nodes(_, _ []float64) bool

func (GPD) Quantile 

func (d GPD) Quantile(p float64) float64

Quantile works from p directly, so the lower tail keeps its precision.

func (GPD) QuantileUpper 

func (d GPD) QuantileUpper(q float64) float64

func (GPD) Support 

func (d GPD) Support() (lo, hi float64)

func (GPD) Survival 

func (d GPD) Survival(x float64) float64

func (GPD) Var 

func (d GPD) Var() float64

Var is +Inf for xi ≥ ½.

type Gamma 

type Gamma struct {
	// contains filtered or unexported fields
}

Gamma is the Gamma distribution with shape k and scale θ.

func NewGamma 

func NewGamma(shape, scale float64) (Gamma, error)

NewGamma validates shape > 0 and scale > 0.

func NewGammaFromMeanSD 

func NewGammaFromMeanSD(mean, sd float64) (Gamma, error)

NewGammaFromMeanSD converts a mean and standard deviation.

func NewGammaFromShapeRate 

func NewGammaFromShapeRate(shape, rate float64) (Gamma, error)

NewGammaFromShapeRate converts a shape and rate.

func (Gamma) CDF 

func (d Gamma) CDF(x float64) float64

func (Gamma) Fill 

func (d Gamma) Fill(r *rand.Rand, dst []float64)

func (Gamma) Laplace 

func (d Gamma) Laplace(s complex128) (complex128, bool)

Gamma: (1 + θs)^(−k) through the principal logarithm; with Re(s) ≥ 0 the argument has real part at least 1, away from the branch cut.

func (Gamma) Mean 

func (d Gamma) Mean() float64

func (Gamma) Nodes 

func (Gamma) Nodes(_, _ []float64) bool

func (Gamma) Quantile 

func (d Gamma) Quantile(p float64) float64

Quantile inverts the regularised incomplete gamma function to full precision: gonum's inverse seeds a safeguarded Newton iteration, with a small-x series seed where gonum returns 0.

func (Gamma) QuantileUpper 

func (d Gamma) QuantileUpper(q float64) float64

QuantileUpper inverts the survival function the same way.

func (Gamma) Support 

func (d Gamma) Support() (lo, hi float64)

func (Gamma) Survival 

func (d Gamma) Survival(x float64) float64

func (Gamma) Var 

func (d Gamma) Var() float64

type Geometric 

type Geometric struct {
	// contains filtered or unexported fields
}

Geometric counts failures before the first success; support {0, 1, …}.

func NewGeometric 

func NewGeometric(p float64) (Geometric, error)

NewGeometric validates 0 < p ≤ 1.

func (Geometric) CDF 

func (d Geometric) CDF(x float64) float64

CDF is 1 − (1−p)^(⌊k⌋+1).

func (Geometric) Fill 

func (d Geometric) Fill(r *rand.Rand, dst []float64)

func (Geometric) Laplace 

func (Geometric) Laplace(complex128) (complex128, bool)

func (Geometric) Mean 

func (d Geometric) Mean() float64

func (Geometric) Nodes 

func (Geometric) Nodes(_, _ []float64) bool

func (Geometric) PMF 

func (d Geometric) PMF(x float64) float64

func (Geometric) Quantile 

func (d Geometric) Quantile(p float64) float64

Quantile is the smallest k with CDF(k) ≥ p.

func (Geometric) QuantileUpper 

func (d Geometric) QuantileUpper(q float64) float64

QuantileUpper is the smallest k with Survival(k) ≤ q.

func (Geometric) Support 

func (d Geometric) Support() (lo, hi float64)

func (Geometric) Survival 

func (d Geometric) Survival(x float64) float64

func (Geometric) Var 

func (d Geometric) Var() float64

type LogPERT 

type LogPERT struct {
	// contains filtered or unexported fields
}

LogPERT is a PERT on log10 of the value: the draw is 10 to a PERT draw on [log10 low, log10 high] with mode log10 peak.

func NewLogPERT 

func NewLogPERT(low, peak, high, t float64) (LogPERT, error)

NewLogPERT validates like NewPERT and additionally requires low > 0. Its moments are computed once by quadrature.

func (LogPERT) CDF 

func (d LogPERT) CDF(x float64) float64

func (LogPERT) Fill 

func (d LogPERT) Fill(r *rand.Rand, dst []float64)

func (LogPERT) Laplace 

func (LogPERT) Laplace(complex128) (complex128, bool)

func (LogPERT) Mean 

func (d LogPERT) Mean() float64

func (LogPERT) Nodes 

func (LogPERT) Nodes(_, _ []float64) bool

func (LogPERT) Quantile 

func (d LogPERT) Quantile(p float64) float64

func (LogPERT) QuantileUpper 

func (d LogPERT) QuantileUpper(q float64) float64

func (LogPERT) Support 

func (d LogPERT) Support() (lo, hi float64)

func (LogPERT) Survival 

func (d LogPERT) Survival(x float64) float64

func (LogPERT) Var 

func (d LogPERT) Var() float64

type LogUniform 

type LogUniform struct {
	// contains filtered or unexported fields
}

LogUniform is uniform in the logarithm on [a, b].

func NewLogUniform 

func NewLogUniform(a, b float64) (LogUniform, error)

NewLogUniform validates 0 < a < b.

func (LogUniform) CDF 

func (d LogUniform) CDF(x float64) float64

func (LogUniform) Fill 

func (d LogUniform) Fill(r *rand.Rand, dst []float64)

func (LogUniform) Laplace 

func (LogUniform) Laplace(complex128) (complex128, bool)

func (LogUniform) Mean 

func (d LogUniform) Mean() float64

func (LogUniform) Nodes 

func (LogUniform) Nodes(_, _ []float64) bool

func (LogUniform) Quantile 

func (d LogUniform) Quantile(p float64) float64

func (LogUniform) QuantileUpper 

func (d LogUniform) QuantileUpper(q float64) float64

func (LogUniform) Support 

func (d LogUniform) Support() (lo, hi float64)

func (LogUniform) Survival 

func (d LogUniform) Survival(x float64) float64

func (LogUniform) Var 

func (d LogUniform) Var() float64

type Lognormal 

type Lognormal struct {
	// contains filtered or unexported fields
}

Lognormal is exp of a Normal(mu, sigma).

func NewLognormal 

func NewLognormal(mu, sigma float64) (Lognormal, error)

NewLognormal validates sigma > 0 and a finite mu.

func NewLognormalFromMeanSD 

func NewLognormalFromMeanSD(mean, sd float64) (Lognormal, error)

NewLognormalFromMeanSD converts a mean and standard deviation.

func NewLognormalFromMedianP90 

func NewLognormalFromMedianP90(median, p90 float64) (Lognormal, error)

NewLognormalFromMedianP90 converts a median and a 90th percentile.

func (Lognormal) CDF 

func (d Lognormal) CDF(x float64) float64

func (Lognormal) Fill 

func (d Lognormal) Fill(r *rand.Rand, dst []float64)

func (Lognormal) Laplace 

func (Lognormal) Laplace(complex128) (complex128, bool)

func (Lognormal) Mean 

func (d Lognormal) Mean() float64

func (Lognormal) Nodes 

func (Lognormal) Nodes(_, _ []float64) bool

func (Lognormal) Quantile 

func (d Lognormal) Quantile(p float64) float64

func (Lognormal) QuantileUpper 

func (d Lognormal) QuantileUpper(q float64) float64

func (Lognormal) Support 

func (d Lognormal) Support() (lo, hi float64)

func (Lognormal) Survival 

func (d Lognormal) Survival(x float64) float64

func (Lognormal) Var 

func (d Lognormal) Var() float64

type NegativeBinomial 

type NegativeBinomial struct {
	// contains filtered or unexported fields
}

NegativeBinomial counts failures before the r-th success with success probability p; r is real. It is drawn exactly as Poisson(Gamma(r, (1−p)/p)).

func NewNegativeBinomial 

func NewNegativeBinomial(r, p float64) (NegativeBinomial, error)

NewNegativeBinomial validates r > 0 and 0 < p < 1.

func NewNegativeBinomialFromMeanSize 

func NewNegativeBinomialFromMeanSize(mean, size float64) (NegativeBinomial, error)

NewNegativeBinomialFromMeanSize converts a mean and size: r = size, p = size/(size + mean), so Var = mean + mean²/size.

func (NegativeBinomial) CDF 

func (d NegativeBinomial) CDF(x float64) float64

CDF is P(K ≤ k) = I_p(r, ⌊k⌋ + 1).

func (NegativeBinomial) Fill 

func (d NegativeBinomial) Fill(r *rand.Rand, dst []float64)

func (NegativeBinomial) Laplace 

func (NegativeBinomial) Laplace(complex128) (complex128, bool)

func (NegativeBinomial) Mean 

func (d NegativeBinomial) Mean() float64

func (NegativeBinomial) Nodes 

func (NegativeBinomial) Nodes(_, _ []float64) bool

func (NegativeBinomial) PMF 

func (d NegativeBinomial) PMF(x float64) float64

func (NegativeBinomial) Quantile 

func (d NegativeBinomial) Quantile(p float64) float64

Quantile is the smallest k with CDF(k) ≥ p, by bracketing and bisection.

func (NegativeBinomial) QuantileUpper 

func (d NegativeBinomial) QuantileUpper(q float64) float64

QuantileUpper is the smallest k with Survival(k) ≤ q.

func (NegativeBinomial) Support 

func (d NegativeBinomial) Support() (lo, hi float64)

func (NegativeBinomial) Survival 

func (d NegativeBinomial) Survival(x float64) float64

func (NegativeBinomial) Var 

func (d NegativeBinomial) Var() float64

type Normal 

type Normal struct {
	// contains filtered or unexported fields
}

Normal is the normal distribution; its support is the whole line, so it needs truncation before it can sit in a model slot.

func NewNormal 

func NewNormal(mu, sigma float64) (Normal, error)

NewNormal validates sigma > 0 and a finite mu.

func (Normal) CDF 

func (d Normal) CDF(x float64) float64

func (Normal) Fill 

func (d Normal) Fill(r *rand.Rand, dst []float64)

func (Normal) Laplace 

func (Normal) Laplace(complex128) (complex128, bool)

func (Normal) Mean 

func (d Normal) Mean() float64

func (Normal) Nodes 

func (Normal) Nodes(_, _ []float64) bool

func (Normal) Quantile 

func (d Normal) Quantile(p float64) float64

func (Normal) QuantileUpper 

func (d Normal) QuantileUpper(q float64) float64

func (Normal) Support 

func (d Normal) Support() (lo, hi float64)

func (Normal) Survival 

func (d Normal) Survival(x float64) float64

func (Normal) Var 

func (d Normal) Var() float64

type PERT 

type PERT struct {
	// contains filtered or unexported fields
}

PERT is the modified PERT distribution on [low, high] with mode peak and shape parameter t.

func NewPERT 

func NewPERT(low, peak, high, t float64) (PERT, error)

NewPERT validates low ≤ peak ≤ high, all finite with a positive finite span, and t ≥ 0 (t = 0 is the uniform).

Example

A PERT is built from its low, most likely and high values; the fourth parameter is the shape, usually dist.DefaultPERTShape. 

package main

import (
	"fmt"
	"math"

	"code.eitanity.com/variate/dist"
)

func main() {
	d, err := dist.NewPERT(1000, 2500, 9000, dist.DefaultPERTShape)
	if err != nil {
		fmt.Println(err)
		return
	}
	lo, hi := d.Support()
	fmt.Printf("mean %.1f  sd %.1f  support [%g, %g]\n", d.Mean(), math.Sqrt(d.Var()), lo, hi)
	fmt.Printf("P(X <= 2500) = %.4f\n", d.CDF(2500))
}

Output:
mean 3333.3  sd 1374.4  support [1000, 9000]
P(X <= 2500) = 0.3216

func (PERT) CDF 

func (d PERT) CDF(x float64) float64

func (PERT) Fill 

func (d PERT) Fill(r *rand.Rand, dst []float64)

func (PERT) Laplace 

func (PERT) Laplace(complex128) (complex128, bool)

func (PERT) Mean 

func (d PERT) Mean() float64

func (PERT) Nodes 

func (d PERT) Nodes(x, w []float64) bool

func (PERT) Quantile 

func (d PERT) Quantile(p float64) float64

func (PERT) QuantileUpper 

func (d PERT) QuantileUpper(q float64) float64

func (PERT) Shape 

func (d PERT) Shape() (alpha, beta float64)

Shape returns the Beta shapes behind the PERT.

func (PERT) Support 

func (d PERT) Support() (lo, hi float64)

func (PERT) Survival 

func (d PERT) Survival(x float64) float64

func (PERT) Var 

func (d PERT) Var() float64

type PMFer 

type PMFer interface {
	PMF(x float64) float64
}

PMFer is implemented by discrete distributions. Values are integers stored as float64, except for Categorical and Empirical.

type Pareto 

type Pareto struct {
	// contains filtered or unexported fields
}

Pareto has minimum xm and tail index alpha.

func NewPareto 

func NewPareto(xm, alpha float64) (Pareto, error)

NewPareto validates xm > 0 and alpha > 0.

func (Pareto) CDF 

func (d Pareto) CDF(x float64) float64

func (Pareto) Fill 

func (d Pareto) Fill(r *rand.Rand, dst []float64)

func (Pareto) Laplace 

func (Pareto) Laplace(complex128) (complex128, bool)

func (Pareto) Mean 

func (d Pareto) Mean() float64

Mean is +Inf for alpha ≤ 1.

func (Pareto) Nodes 

func (Pareto) Nodes(_, _ []float64) bool

func (Pareto) Quantile 

func (d Pareto) Quantile(p float64) float64

func (Pareto) QuantileUpper 

func (d Pareto) QuantileUpper(q float64) float64

func (Pareto) Support 

func (d Pareto) Support() (lo, hi float64)

func (Pareto) Survival 

func (d Pareto) Survival(x float64) float64

func (Pareto) Var 

func (d Pareto) Var() float64

Var is +Inf for alpha ≤ 2.

type Poisson 

type Poisson struct {
	// contains filtered or unexported fields
}

Poisson is the Poisson distribution with a fixed rate.

func NewPoisson 

func NewPoisson(lambda float64) (Poisson, error)

NewPoisson validates lambda ≥ 0 and finite.

func (Poisson) CDF 

func (d Poisson) CDF(x float64) float64

func (Poisson) Fill 

func (d Poisson) Fill(r *rand.Rand, dst []float64)

func (Poisson) Laplace 

func (Poisson) Laplace(complex128) (complex128, bool)

func (Poisson) Mean 

func (d Poisson) Mean() float64

func (Poisson) Nodes 

func (Poisson) Nodes(_, _ []float64) bool

func (Poisson) PMF 

func (d Poisson) PMF(x float64) float64

PMF returns P(K = x); zero off the integers.

func (Poisson) Quantile 

func (d Poisson) Quantile(p float64) float64

func (Poisson) QuantileUpper 

func (d Poisson) QuantileUpper(q float64) float64

func (Poisson) Support 

func (d Poisson) Support() (lo, hi float64)

func (Poisson) Survival 

func (d Poisson) Survival(x float64) float64

func (Poisson) Var 

func (d Poisson) Var() float64

type Quantiler 

type Quantiler interface {
	Quantile(p float64) float64
	Survival(x float64) float64
	QuantileUpper(q float64) float64
}

Quantiler is implemented by every continuous distribution. Survival and QuantileUpper work on the upper tail directly so that no precision is lost to 1 − CDF.

type Sampler 

type Sampler struct {
	// contains filtered or unexported fields
}

Sampler is a pool of pre-drawn values for one distribution. Every call to Next consumes one value; when the pool is used up it is refilled with fresh draws, never reused.

func (*Sampler) Next 

func (s *Sampler) Next() float64

Next returns the next pre-drawn value, refilling the pool when empty.

type SamplerSet 

type SamplerSet struct {
	// contains filtered or unexported fields
}

SamplerSet holds one Sampler per compiled distribution plus the control stream, all backed by one slab allocated once. It is reused across tasks by Reset.

Example

Draws come through a Sampler, which refills a buffer from the distribution's Fill and hands out one value per Next. A SamplerSet gives every distribution its own stream for a seed and task. 

package main

import (
	"fmt"

	"code.eitanity.com/variate/dist"
)

func main() {
	d, _ := dist.NewPERT(1, 2, 4, dist.DefaultPERTShape)
	set := dist.NewSamplerSet([]dist.Distribution{d}, 1024)
	set.Reset(7, 0)
	s := set.Sampler(0)
	sum := 0.0
	for i := 0; i < 100000; i++ {
		sum += s.Next()
	}
	fmt.Printf("sample mean %.2f, exact %.2f\n", sum/100000, d.Mean())
}

Output:
sample mean 2.17, exact 2.17

func NewSamplerSet 

func NewSamplerSet(dists []Distribution, poolSize int) *SamplerSet

NewSamplerSet allocates the pools: poolSize values per distribution.

func (*SamplerSet) Control 

func (ss *SamplerSet) Control() *rand.Rand

Control returns the task's control stream.

func (*SamplerSet) Len 

func (ss *SamplerSet) Len() int

Len returns the number of distributions.

func (*SamplerSet) Reset 

func (ss *SamplerSet) Reset(seed uint64, task uint32)

Reset re-seeds every stream for task j under seed and empties the pools. Distribution k uses the key splitmix64(j<<32 | k); the control stream uses k = len(dists), one past the last distribution. It allocates nothing.

func (*SamplerSet) Sampler 

func (ss *SamplerSet) Sampler(k int) *Sampler

Sampler returns the pool of distribution k.

type Scaled added in v0.1.3 

type Scaled struct {
	// contains filtered or unexported fields
}

Scaled is f·X for a factor f > 0: every draw of X multiplied by f, from the same stream, so a scaled model draws what the unscaled one does, value for value, times f.

func NewScaled added in v0.1.3 

func NewScaled(d Distribution, f float64) (Scaled, error)

NewScaled validates that f is finite and positive.

func (Scaled) Base added in v0.1.3 

func (d Scaled) Base() Distribution

Base is X.

func (Scaled) CDF added in v0.1.3 

func (d Scaled) CDF(x float64) float64

func (Scaled) Factor added in v0.1.3 

func (d Scaled) Factor() float64

Factor is f.

func (Scaled) Fill added in v0.1.3 

func (d Scaled) Fill(r *rand.Rand, dst []float64)

func (Scaled) Laplace added in v0.1.3 

func (d Scaled) Laplace(s complex128) (complex128, bool)

Laplace is E[e^{−s·f·X}], X's transform at f·s.

func (Scaled) Mean added in v0.1.3 

func (d Scaled) Mean() float64

func (Scaled) Nodes added in v0.1.3 

func (d Scaled) Nodes(x, w []float64) bool

Nodes are X's nodes times f, with X's weights.

func (Scaled) Quantile added in v0.1.3 

func (d Scaled) Quantile(p float64) float64

func (Scaled) QuantileUpper added in v0.1.3 

func (d Scaled) QuantileUpper(q float64) float64

func (Scaled) Support added in v0.1.3 

func (d Scaled) Support() (lo, hi float64)

func (Scaled) Survival added in v0.1.3 

func (d Scaled) Survival(x float64) float64

func (Scaled) Var added in v0.1.3 

func (d Scaled) Var() float64

type Triangular 

type Triangular struct {
	// contains filtered or unexported fields
}

Triangular is the triangular distribution on [low, high] with the given mode. The closed forms are written so that nothing cancels when the mode sits at an end of the range.

func NewTriangular 

func NewTriangular(low, mode, high float64) (Triangular, error)

NewTriangular validates low ≤ mode ≤ high with low < high, all finite.

func (Triangular) CDF 

func (d Triangular) CDF(x float64) float64

func (Triangular) Fill 

func (d Triangular) Fill(r *rand.Rand, dst []float64)

func (Triangular) Laplace 

func (Triangular) Laplace(complex128) (complex128, bool)

func (Triangular) Mean 

func (d Triangular) Mean() float64

func (Triangular) Nodes 

func (Triangular) Nodes(_, _ []float64) bool

func (Triangular) Quantile 

func (d Triangular) Quantile(p float64) float64

func (Triangular) QuantileUpper 

func (d Triangular) QuantileUpper(q float64) float64

func (Triangular) Support 

func (d Triangular) Support() (lo, hi float64)

func (Triangular) Survival 

func (d Triangular) Survival(x float64) float64

func (Triangular) Var 

func (d Triangular) Var() float64

type Truncated 

type Truncated struct {
	// contains filtered or unexported fields
}

Truncated restricts a continuous distribution to [lo, hi] and renormalises. Draws are by inversion on the side of the range that keeps its precision, so it costs one quantile evaluation per draw.

func NewSplit added in v0.2.0 

func NewSplit(d Distribution, t float64, above bool) (half Truncated, mass float64, err error)

NewSplit returns the half of d that a threshold at t keeps: X given X > t when above is set, else X given X ≤ t, so an atom at t goes below. mass is the half's probability, P(X > t) or P(X ≤ t); when it is 0 the half is empty and the Truncated is the zero value. The moments are summed for a finite or an integer family and taken by quadrature in probability units otherwise, which an atom does not disturb: the probability range holds it on the side it belongs to.

func NewTruncated 

func NewTruncated(d Continuous, lo, hi float64) (Truncated, error)

NewTruncated validates lo < hi, that the range keeps at least 1e-9 of the mass, and computes the moments by quadrature.

Example

Truncation restricts a distribution to an interval and renormalises; capping clamps draws at a ceiling, leaving an atom there. 

package main

import (
	"fmt"

	"code.eitanity.com/variate/dist"
)

func main() {
	base, _ := dist.NewLognormalFromMedianP90(4, 24)
	t, err := dist.NewTruncated(base, 1, 48)
	if err != nil {
		fmt.Println(err)
		return
	}
	c, _ := dist.NewCapped(base, 48)
	fmt.Printf("lognormal mean %.2f\n", base.Mean())
	fmt.Printf("truncated to [1, 48]: mean %.2f, P(X < 1) = %.0f\n", t.Mean(), t.CDF(1))
	fmt.Printf("capped at 48: mean %.2f, P(X = 48) = %.3f\n", c.Mean(), 1-c.CDF(47.999999))
}

Output:
lognormal mean 10.63
truncated to [1, 48]: mean 8.48, P(X < 1) = 0
capped at 48: mean 8.70, P(X = 48) = 0.038

func (Truncated) CDF 

func (d Truncated) CDF(x float64) float64

func (Truncated) Fill 

func (d Truncated) Fill(r *rand.Rand, dst []float64)

func (Truncated) Laplace 

func (Truncated) Laplace(complex128) (complex128, bool)

func (Truncated) Mean 

func (d Truncated) Mean() float64

func (Truncated) Nodes 

func (Truncated) Nodes(_, _ []float64) bool

func (Truncated) Quantile 

func (d Truncated) Quantile(p float64) float64

func (Truncated) QuantileUpper 

func (d Truncated) QuantileUpper(q float64) float64

func (Truncated) Support 

func (d Truncated) Support() (lo, hi float64)

func (Truncated) Survival 

func (d Truncated) Survival(x float64) float64

func (Truncated) Var 

func (d Truncated) Var() float64

type TruncatedNormal 

type TruncatedNormal struct {
	// contains filtered or unexported fields
}

TruncatedNormal is Normal(mu, sigma) restricted to [lo, hi]; either bound may be infinite.

func NewTruncatedNormal 

func NewTruncatedNormal(mu, sigma, lo, hi float64) (TruncatedNormal, error)

NewTruncatedNormal validates sigma > 0, lo < hi, and that the interval keeps a representable mass: both standardised bounds within ±37 unless infinite.

func (TruncatedNormal) CDF 

func (d TruncatedNormal) CDF(x float64) float64

func (TruncatedNormal) Fill 

func (d TruncatedNormal) Fill(r *rand.Rand, dst []float64)

func (TruncatedNormal) Laplace 

func (TruncatedNormal) Laplace(complex128) (complex128, bool)

func (TruncatedNormal) Mean 

func (d TruncatedNormal) Mean() float64

func (TruncatedNormal) Nodes 

func (TruncatedNormal) Nodes(_, _ []float64) bool

func (TruncatedNormal) Quantile 

func (d TruncatedNormal) Quantile(p float64) float64

func (TruncatedNormal) QuantileUpper 

func (d TruncatedNormal) QuantileUpper(q float64) float64

func (TruncatedNormal) Support 

func (d TruncatedNormal) Support() (lo, hi float64)

func (TruncatedNormal) Survival 

func (d TruncatedNormal) Survival(x float64) float64

func (TruncatedNormal) Var 

func (d TruncatedNormal) Var() float64

type Uniform 

type Uniform struct {
	// contains filtered or unexported fields
}

Uniform is the continuous uniform on [a, b].

func NewUniform 

func NewUniform(a, b float64) (Uniform, error)

NewUniform validates a < b, both finite, with a finite span.

func (Uniform) CDF 

func (d Uniform) CDF(x float64) float64

func (Uniform) Fill 

func (d Uniform) Fill(r *rand.Rand, dst []float64)

func (Uniform) Laplace 

func (d Uniform) Laplace(s complex128) (complex128, bool)

func (Uniform) Mean 

func (d Uniform) Mean() float64

func (Uniform) Nodes 

func (d Uniform) Nodes(x, w []float64) bool

func (Uniform) Quantile 

func (d Uniform) Quantile(p float64) float64

func (Uniform) QuantileUpper 

func (d Uniform) QuantileUpper(q float64) float64

func (Uniform) Support 

func (d Uniform) Support() (lo, hi float64)

func (Uniform) Survival 

func (d Uniform) Survival(x float64) float64

func (Uniform) Var 

func (d Uniform) Var() float64

type Weibull 

type Weibull struct {
	// contains filtered or unexported fields
}

Weibull has shape k and scale lambda.

func NewWeibull 

func NewWeibull(shape, scale float64) (Weibull, error)

NewWeibull validates shape > 0 and scale > 0.

func (Weibull) CDF 

func (d Weibull) CDF(x float64) float64

func (Weibull) Fill 

func (d Weibull) Fill(r *rand.Rand, dst []float64)

func (Weibull) Laplace 

func (Weibull) Laplace(complex128) (complex128, bool)

func (Weibull) Mean 

func (d Weibull) Mean() float64

func (Weibull) Nodes 

func (Weibull) Nodes(_, _ []float64) bool

func (Weibull) Quantile 

func (d Weibull) Quantile(p float64) float64

func (Weibull) QuantileUpper 

func (d Weibull) QuantileUpper(q float64) float64

func (Weibull) Support 

func (d Weibull) Support() (lo, hi float64)

func (Weibull) Survival 

func (d Weibull) Survival(x float64) float64

func (Weibull) Var 

func (d Weibull) Var() float64

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