RTMBdist (version 0.1.0)

t2: Student t distribution with location and scale

Description

Density, distribution function, quantile function, and random generation for the t distribution with location and scale parameters.

Usage

dt2(x, mu, sigma, df, log = FALSE)
pt2(q, mu, sigma, df)
rt2(n, mu, sigma, df)
qt2(p, mu, sigma, df)
pt(q, df)

Value

dt2 gives the density, pt2 gives the distribution function, qt2 gives the quantile function, and rt2 generates random deviates.

Arguments

x, q

vector of quantiles

mu

location parameter

sigma

scale parameter, must be positive.

df

degrees of freedom, must be positive.

log

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

n

number of random values to return.

p

vector of probabilities

Details

This implementation of dt2 allows for automatic differentiation with RTMB.

Examples

x <- rt2(1, 1, 2, 5)
d <- dt2(x, 1, 2, 5)
p <- pt2(x, 1, 2, 5)
q <- qt2(p, 1, 2, 5)