t2: Student t distribution with location and scale

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

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, lower.tail = TRUE, log.p = FALSE)

rt2(n, mu, sigma, df)

qt2(p, mu, sigma, df, lower.tail = TRUE, log.p = FALSE)

pt.ad(q, df)

Arguments

x, q	vector of quantiles
mu	location parameter
sigma	scale parameter, must be positive.
df	degrees of freedom, must be positive.
log, log.p	logical; if TRUE, probabilities/ densities p are returned as \log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X \le x], otherwise P[X > x].
n	number of random values to return.
p	vector of probabilities

Details

This implementation of dt2 allows for automatic differentiation with RTMB.

f(x;\,\mu,\sigma,\nu) = \frac{1}{\sigma}\,f_t\!\left(\frac{x-\mu}{\sigma};\,\nu\right),

where f_t(\cdot;\nu) is the Student-t PDF with \nu degrees of freedom.

Value

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

pt.ad is an AD-compatible replacement for stats::pt. It is used internally and is reached automatically whenever an argument is an AD variable, so stats::pt is left untouched for ordinary use.

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)

RTMBdist documentation built on Oct. 31, 2026, 5:07 p.m.