StudentTDistribution

Model a zero-mean Student’s t-distribution with scale \(\sigma\) and degrees of freedom \(\nu\).

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Declaration

classdef StudentTDistribution < Distribution

Overview

StudentTDistribution implements the Student’s t-distribution with density \(p(z) = \frac{\Gamma\!\left(\frac{\nu+1}{2}\right)} {\sqrt{\pi \nu}\,\sigma\,\Gamma\!\left(\frac{\nu}{2}\right)} \left(1 + \frac{z^{2}}{\nu \sigma^{2}}\right)^{-\frac{\nu+1}{2}},\) cumulative distribution \(F(z)\) given by the corresponding Student-t CDF, and variance \(\mathrm{variance} = \frac{\nu \sigma^{2}}{\nu-2}\) for \(\nu > 2.\) The constructor accepts either the scale parameter sigma or the total variance, but not both.

distribution = StudentTDistribution(nu=4.5, sigma=8.5);

Topics

• Create distributions
  • StudentTDistribution Create a Student’s t-distribution from scale or variance.
• Inspect distribution properties
  • nu Degrees of freedom \(\nu\).
  • sigma Scale parameter \(\sigma\).

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