distr (version 1.5)

Td-class: Class "Td"

Description

The $t$ distribution with df $= \nu$ degrees of freedom has density $$f(x) = \frac{\Gamma ((\nu+1)/2)}{\sqrt{\pi \nu} \Gamma (\nu/2)} (1 + x^2/\nu)^{-(\nu+1)/2}$$ for all real $x$. It has mean $0$ (for $\nu > 1$) and variance $\frac{\nu}{\nu-2}$ (for $\nu > 2$). C.f. rt

docTdype

class

Objects from the Class

Objects can be created by calls of the form Td(df). This object is a $t$ distribution.

Extends

Class "AbscontDistribution", directly. Class "UnivariateDistribution", by class "AbscontDistribution". Class "Distribution", by class "AbscontDistribution".

See Also

TParameter-class AbscontDistribution-class Reals-class rt

Examples

T <- Td(df = 1) # T is a t distribution with df = 1.
r(T)(1) # one random number generated from this distribution, e.g. -0.09697573
d(T)(1) # Density of this distribution is 0.1591549 for x = 1.
p(T)(1) # Probability that x < 1 is 0.75.
q(T)(.1) # Probability that x < -3.077684 is 0.1.
df(T) # df of this distribution is 1.
df(T) <- 2 # df of this distribution is now 2.

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