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Student t Distribution

docs/tutorial:stats:continuous_t

There is one shape parameter $ν > 0$ and the support is $x \in R$ .

where $I (x; a, b)$ is the incomplete beta integral and $I^{- 1} (I (x; a, b); a, b) = x$ . As $ν \to \infty,$ this distribution approaches the standard normal distribution.

h [X] = \frac{ν + 1}{2} [ψ (\frac{1 + ν}{2}) - ψ (\frac{ν}{2})] + ln [ν B (\frac{ν}{2}, \frac{1}{2})]

where $ψ (x)$ is the digamma function and $B (x, y)$ is the beta function.

References

"Student's t-distribution", Wikipedia, https://en.wikipedia.org/wiki/Student%27s_t-distribution

Implementation: scipy.stats.t