lestat (version 1.9)

tdistribution: A t-distribution

Description

Create an object representing a univariate non-centered t-distribution.

Usage

tdistribution(expectation = 0, degreesoffreedom = 1e+20, 
    lambda, P = 1)

Arguments

expectation

The expectation of the distribution.

degreesoffreedom

The degrees of freedom parameter.

lambda

The natural logarithm of the scale \(\sigma\) of the distribution. The standard t-distribution has scale 1, and the default for lambda is \(\log(1)=0\).

P

An alternative to specifying the logged scale \(\log(\sigma)\) with lambda is to specify P: It is defined as \(P=1/\sigma^2\).

Value

A t-distribution.

Details

The probability density of a t-distribution with expectation \(\mu\), degrees of freedom \(\nu\), and logged scale \(\lambda\) is proportional to $$ f(x)=(\nu + e^{-2\lambda}(x-\mu)^2)^{-(\nu+1)/2} $$

See Also

mtdistribution

Examples

# NOT RUN {
dist <- tdistribution(3)
plot(dist)
# }