BUILT-IN MATHEMATICA SYMBOL

RandomVariate

RandomVariate[dist]
gives a pseudorandom variate from the symbolic distribution dist.

RandomVariate

gives a list of n pseudorandom variates from the symbolic distribution dist.

RandomVariate

gives an

array of pseudorandom variates from the symbolic distribution dist.

MORE INFORMATION

RandomVariate can generate random variates for continuous, discrete, or mixed distributions specified as a symbolic distribution.

RandomVariate gives a different sequence of pseudorandom numbers whenever you run Mathematica. You can start with a particular seed using SeedRandom.

With the setting WorkingPrecision->p, random numbers of precision p will be generated.

EXAMPLES

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Basic Examples (5)

Simulate a continuous probability distribution:

Simulate a discrete probability distribution:

Simulate a multivariate continuous distribution:

Simulate a multivariate discrete distribution:

Generate random numbers from a mixture distribution:

Simulate a continuous probability distribution:

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Simulate a discrete probability distribution:

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Simulate a multivariate continuous distribution:

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Simulate a multivariate discrete distribution:

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Generate random numbers from a mixture distribution:

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Scope (21)

Use RandomVariate to generate arrays of different sizes and dimensions:

A vector:

A matrix:

A rank-3 tensor:

Generate high-precision random variates:

Use SeedRandom to get repeatable random values:

Generate random variates for a univariate continuous distribution:

Discrete univariate distribution:

Continuous multivariate distribution:

Discrete multivariate distribution:

Generate random variates for univariate continuous distributions:

Generate random variates for univariate discrete distributions:

Generate random variates for multivariate continuous distributions:

Generate random variates for multivariate discrete distributions:

Generate random variates for a univariate EmpiricalDistribution:

Using a multivariate empirical distribution:

Using a univariate HistogramDistribution:

A multivariate histogram distribution:

Using a univariate KernelMixtureDistribution:

Using censored data with SurvivalDistribution:

Generate random variates for a TransformedDistribution:

An equivalent way of generating the same random variates:

Generate random variates for a ProductDistribution:

An equivalent way of generating the same random variates:

Using a component mixture of normal distributions:

Parameter mixture of exponential distributions:

Compare the variance of the sample with the variance of the distribution:

Truncated normal distribution:

Censored exponential distribution:

Compare the kurtosis for the sample with the kurtosis for the distribution:

Marginal distribution:

Compute probabilities using the sample and the marginal distribution:

Copula distribution:

Compare the value of a moment for the sample with that for the copula distribution:

Formula distribution:

Options (1)

By default MachinePrecision random numbers are generated for continuous distributions:

Use the WorkingPrecision option to generate numbers with arbitrary precision:

Applications (17)

Generate random data for a continuous distribution and compare its histogram to the PDF:

Generate random data for a discrete distribution and compare its histogram to the PDF:

Generate random data for a bivariate distribution and compare its histogram to the PDF:

Compare the plots of random data for continuous multivariate distributions:

Consider vectors with standard normal components:

The angle will follow a uniform distribution:

The norm will follow a Rayleigh distribution:

Consider three-dimensional vectors with standard normal components:

The

angle in spherical coordinates follows a uniform distribution:

The norm will follow a

distribution:

Verify the Poisson approximation to the binomial distribution using random variates:

Define a truncated triangular distribution:

Generate random numbers from this distribution:

Mean, variance, and kurtosis:

Moments:

Probabilities and expectations:

Simulate the distribution of a function of a random variable:

Compare the mean and variance of the sample with those for the distribution:

Generate random data from a normal distribution:

Define nonparametric distributions using this data:

Compare the mean and variance of these distributions:

Simulate 10 throws of a fair six-sided die:

Simulate seven throws of a pair of fair six-sided dice:

A coin-tossing experiment consists of tossing a fair coin repeatedly until a head results. Simulate the process:

A radioactive material on average emits 3.2

-particles per second; show the distribution. Simulate a typical particle-count experiment for 10 minutes:

Simulate a symmetric random walk with values

and

:

Generate random data for a normal distribution:

Estimate the distribution parameters using the random data:

Generate high-precision random data for a component mixture distribution:

Estimate the mixture probabilities, assuming the component distributions are known:

Given a binormal sample, the

-statistic follows a shifted FisherZDistribution:

Generate the distribution of

-statistics for binormal samples of size

:

Visually compare the

-statistic distribution to a shifted FisherZDistribution:

DistributionFitTest confirms the result:

Properties & Relations (16)

RandomInteger generates uniform discrete random variates:

RandomReal generates uniform continuous variates:

RandomChoice generates random choices with replacement from a list:

RandomSample generates random choice without replacement from a list:

RandomPrime generates a random prime number:

RandomImage generates a random image:

RandomGraph generates a random graph:

Test whether the mean or median is zero by using LocationTest:

Compare means or medians for several datasets using LocationEquivalenceTest:

Test whether two datasets have the same variance by using VarianceTest:

Test whether several datasets have the same variance by using VarianceEquivalenceTest:

Use DistributionFitTest to test goodness of fit between random data and a distribution:

Estimate distribution parameters from random data using EstimatedDistribution:

Estimate nonparametric distributions from random data:

Compare random data to distributions using statistical visualization functions:

Compare multiple distributions using statistical charts:

Plot histograms from random data:

Plot smooth kernel density estimates from data:

Possible Issues (2)

The speed of random variate generation may depend on the distribution:

The WorkingPrecision option is ignored for discrete distributions: