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All functions on this page are accessed via the np.random namespace and use the global MT19937 generator. The same distributions are also available on Generator instances (see Generator API).

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Continuous Distributions

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uniform

Draw samples from a uniform distribution over [low, high). 
function uniform(low?: number, high?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
lownumber0Lower boundary (inclusive).
highnumber1Upper boundary (exclusive).
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Samples from the uniform distribution. 
import * as np from 'numpy-ts';

const a = np.random.uniform(-1, 1, [2, 3]);

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normal

Draw samples from a normal (Gaussian) distribution. 
function normal(loc?: number, scale?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
locnumber0Mean of the distribution.
scalenumber1Standard deviation (spread).
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Samples from the normal distribution. 
import * as np from 'numpy-ts';

const samples = np.random.normal(0, 1, [1000]);

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standard_normal

Draw samples from the standard normal distribution (mean=0, std=1). Equivalent to normal(0, 1, size). 
function standard_normal(size?: number | number[]): NDArray | number
NameTypeDefaultDescription
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Standard normal samples.

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exponential

Draw samples from an exponential distribution. 
function exponential(scale?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
scalenumber1Scale parameter (beta = 1/lambda).
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Exponential samples. 
import * as np from 'numpy-ts';

const a = np.random.exponential(2.0, [1000]);

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standard_exponential

Draw samples from the standard exponential distribution (scale=1). Equivalent to exponential(1, size). 
function standard_exponential(size?: number | number[]): NDArray | number
NameTypeDefaultDescription
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Standard exponential samples.

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gamma

Draw samples from a Gamma distribution. Uses Marsaglia and Tsang’s method. 
function gamma(shape: number, scale?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
shapenumber—Shape parameter (k, alpha). Must be > 0.
scalenumber1Scale parameter (theta). Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Gamma-distributed samples. 
import * as np from 'numpy-ts';

const a = np.random.gamma(2, 2, [1000]);

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standard_gamma

Draw samples from the standard Gamma distribution (scale=1). 
function standard_gamma(shape: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
shapenumber—Shape parameter (alpha). Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Standard gamma samples.

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beta

Draw samples from a Beta distribution. 
function beta(a: number, b: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
anumber—Alpha parameter. Must be > 0.
bnumber—Beta parameter. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Beta-distributed samples in [0, 1]. 
import * as np from 'numpy-ts';

const a = np.random.beta(2, 5, [1000]);

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chisquare

Draw samples from a chi-square distribution. Internally uses gamma(df/2, 2). 
function chisquare(df: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
dfnumber—Degrees of freedom. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Chi-square samples.

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noncentral_chisquare

Draw samples from a noncentral chi-square distribution. 
function noncentral_chisquare(df: number, nonc: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
dfnumber—Degrees of freedom. Must be > 0.
noncnumber—Non-centrality parameter. Must be >= 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Noncentral chi-square samples.

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f

Draw samples from an F distribution. 
function f(dfnum: number, dfden: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
dfnumnumber—Degrees of freedom in numerator. Must be > 0.
dfdennumber—Degrees of freedom in denominator. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — F-distributed samples.

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noncentral_f

Draw samples from a noncentral F distribution. 
function noncentral_f(
  dfnum: number,
  dfden: number,
  nonc: number,
  size?: number | number[]
): NDArray | number
NameTypeDefaultDescription
dfnumnumber—Degrees of freedom in numerator. Must be > 0.
dfdennumber—Degrees of freedom in denominator. Must be > 0.
noncnumber—Non-centrality parameter. Must be >= 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Noncentral F samples.

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standard_cauchy

Draw samples from a standard Cauchy distribution (location=0, scale=1). 
function standard_cauchy(size?: number | number[]): NDArray | number
NameTypeDefaultDescription
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Cauchy samples.

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standard_t

Draw samples from a standard Student’s t distribution. 
function standard_t(df: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
dfnumber—Degrees of freedom. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Student’s t samples.

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laplace

Draw samples from a Laplace (double exponential) distribution. 
function laplace(loc?: number, scale?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
locnumber0Location parameter (mean).
scalenumber1Scale parameter. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Laplace samples.

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logistic

Draw samples from a logistic distribution. 
function logistic(loc?: number, scale?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
locnumber0Location parameter.
scalenumber1Scale parameter. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Logistic samples.

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lognormal

Draw samples from a log-normal distribution. If X ~ Normal(mean, sigma), then exp(X) ~ LogNormal. 
function lognormal(mean?: number, sigma?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
meannumber0Mean of the underlying normal distribution.
sigmanumber1Standard deviation of the underlying normal. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Log-normal samples.

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gumbel

Draw samples from a Gumbel distribution. 
function gumbel(loc?: number, scale?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
locnumber0Location parameter.
scalenumber1Scale parameter. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Gumbel samples.

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pareto

Draw samples from a Pareto II (Lomax) distribution. 
function pareto(a: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
anumber—Shape parameter. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Pareto samples.

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power

Draw samples from a power distribution with positive exponent a - 1 over [0, 1]. 
function power(a: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
anumber—Shape parameter. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Power-distributed samples in [0, 1].

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rayleigh

Draw samples from a Rayleigh distribution. 
function rayleigh(scale?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
scalenumber1Scale parameter. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Rayleigh samples.

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triangular

Draw samples from a triangular distribution over [left, right] with the given mode. 
function triangular(
  left: number,
  mode: number,
  right: number,
  size?: number | number[]
): NDArray | number
NameTypeDefaultDescription
leftnumber—Lower limit.
modenumber—Peak of the distribution. Must satisfy left <= mode <= right.
rightnumber—Upper limit. Must satisfy left < right.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Triangular samples. 
import * as np from 'numpy-ts';

const a = np.random.triangular(0, 5, 10, [1000]);

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wald

Draw samples from a Wald (inverse Gaussian) distribution. 
function wald(mean: number, scale: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
meannumber—Mean of the distribution. Must be > 0.
scalenumber—Scale parameter. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Wald samples.

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weibull

Draw samples from a Weibull distribution. 
function weibull(a: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
anumber—Shape parameter. Must be > 0.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Weibull samples.

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vonmises

Draw samples from a von Mises distribution (circular normal) on the interval [-pi, pi]. 
function vonmises(mu: number, kappa: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
munumber—Mode (center) of the distribution, in radians.
kappanumber—Concentration parameter. Must be >= 0. When kappa = 0, the distribution is uniform on the circle.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Von Mises samples in [-pi, pi].

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Discrete Distributions

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poisson

Draw samples from a Poisson distribution. 
function poisson(lam?: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
lamnumber1Expected number of events (lambda).
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Poisson samples (non-negative integers). 
import * as np from 'numpy-ts';

const a = np.random.poisson(5, [1000]);

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binomial

Draw samples from a binomial distribution. 
function binomial(n: number, p: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
nnumber—Number of trials.
pnumber—Probability of success on each trial.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Binomial samples. 
import * as np from 'numpy-ts';

// 10 coin flips with p=0.5, repeated 1000 times
const a = np.random.binomial(10, 0.5, [1000]);

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geometric

Draw samples from a geometric distribution. Returns the number of trials needed to get the first success. 
function geometric(p: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
pnumber—Probability of success. Must be in (0, 1].
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Geometric samples (positive integers).

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hypergeometric

Draw samples from a hypergeometric distribution. Models drawing nsample items without replacement from a population containing ngood successes and nbad failures. 
function hypergeometric(
  ngood: number,
  nbad: number,
  nsample: number,
  size?: number | number[]
): NDArray | number
NameTypeDefaultDescription
ngoodnumber—Number of good (success) items in the population.
nbadnumber—Number of bad (failure) items in the population.
nsamplenumber—Number of items sampled. Must be <= ngood + nbad.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Number of good items in each sample.

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logseries

Draw samples from a logarithmic series distribution. 
function logseries(p: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
pnumber—Shape parameter. Must be in (0, 1).
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Log-series samples (positive integers).

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negative_binomial

Draw samples from a negative binomial distribution. Models the number of failures before n successes. 
function negative_binomial(n: number, p: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
nnumber—Number of successes. Must be > 0.
pnumber—Probability of success. Must be in (0, 1].
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Negative binomial samples (non-negative integers).

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zipf

Draw samples from a Zipf distribution. 
function zipf(a: number, size?: number | number[]): NDArray | number
NameTypeDefaultDescription
anumber—Distribution parameter. Must be > 1.
sizenumber | number[]undefinedOutput shape.
Returns: NDArray | number — Zipf samples (positive integers).

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Multivariate Distributions

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multinomial

Draw samples from a multinomial distribution. 
function multinomial(n: number, pvals: ArrayLike, size?: number | number[]): NDArray
NameTypeDefaultDescription
nnumber—Number of experiments (total count per sample).
pvalsArrayLike—Probabilities of each category. Must sum to 1 (normalized automatically).
sizenumber | number[]undefinedNumber of multinomial experiments to run.
Returns: NDArray — Array of shape [...size, len(pvals)] with integer counts. 
import * as np from 'numpy-ts';

// 20 rolls of a fair 6-sided die
const a = np.random.multinomial(20, [1/6, 1/6, 1/6, 1/6, 1/6, 1/6]);
// array([3, 4, 2, 5, 3, 3])  (example, sums to 20)

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multivariate_normal

Draw samples from a multivariate normal distribution. 
function multivariate_normal(
  mean: ArrayLike,
  cov: ArrayLike | number[][],
  size?: number | number[],
  check_valid?: 'warn' | 'raise' | 'ignore',
  tol?: number
): NDArray
NameTypeDefaultDescription
meanArrayLike—Mean of the distribution (1-D array of length N).
covArrayLike | number[][]—Covariance matrix (N x N, symmetric positive semi-definite).
sizenumber | number[]undefinedNumber of samples to draw.
check_valid'warn' | 'raise' | 'ignore'undefinedBehavior when covariance is not PSD.
tolnumberundefinedTolerance for covariance validity checks.
Returns: NDArray — Array of shape [...size, N]. 
import * as np from 'numpy-ts';

const mean = [0, 0];
const cov = [[1, 0.5], [0.5, 1]];
const samples = np.random.multivariate_normal(mean, cov, 1000);
// shape [1000, 2]

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dirichlet

Draw samples from a Dirichlet distribution. Each sample is a probability vector that sums to 1. 
function dirichlet(alpha: ArrayLike, size?: number | number[]): NDArray
NameTypeDefaultDescription
alphaArrayLike—Concentration parameters. Must all be > 0 and have at least 2 elements.
sizenumber | number[]undefinedNumber of samples to draw.
Returns: NDArray — Array of shape [...size, len(alpha)], where each row sums to 1. 
import * as np from 'numpy-ts';

const samples = np.random.dirichlet([1, 1, 1], 5);
// shape [5, 3], each row sums to 1.0