Student's t Distribution

Evaluate and generate random samples from Student’s t distribution

Statistics and Machine Learning Toolbox™ offers multiple ways to work with the Student’s t distribution.

  • Use distribution-specific functions with specified distribution parameters. The distribution-specific functions can accept parameters of multiple Student’s t distributions.

  • Use generic distribution functions (cdf, icdf, pdf, random) with a specified distribution name ('T') and parameters.

To learn about the Student's t distribution, see Student's t Distribution.


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cdfCumulative distribution function
icdfInverse cumulative distribution function
pdfProbability density function
randomRandom numbers
randtoolInteractive random number generation
tcdfStudent's t cumulative distribution function
tpdfStudent's t probability density function
tinvStudent's t inverse cumulative distribution function
tstatStudent's t mean and variance
trndStudent's t random numbers
ttestOne-sample and paired-sample t-test
ttest2Two-sample t-test


Student's t Distribution

The Student’s t distribution is a family of curves depending on a single parameter ν (the degrees of freedom).

Generate Cauchy Random Numbers Using Student's t

This example shows how to use the Student's t distribution to generate random numbers from a standard Cauchy distribution.