trunct2: Truncated t distribution with location and scale

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

Truncated t distribution with location and scale

Description

Density, distribution function, quantile function, and random generation for the truncated t distribution with location mu and scale sigma.

Usage

dtrunct2(x, df, mu = 0, sigma = 1, min = -Inf, max = Inf, log = FALSE)

ptrunct2(q, df, mu = 0, sigma = 1, min = -Inf, max = Inf,
         lower.tail = TRUE, log.p = FALSE)

qtrunct2(p, df, mu = 0, sigma = 1, min = -Inf, max = Inf,
         lower.tail = TRUE, log.p = FALSE)

rtrunct2(n, df, mu = 0, sigma = 1, min = -Inf, max = Inf)

Arguments

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

Details

This implementation of dtrunct2 allows for automatic differentiation with RTMB.

f(x;\,\nu,\mu,\sigma,a,b) = \frac{f_t((x-\mu)/\sigma;\,\nu)/\sigma}{F_t((b-\mu)/\sigma;\,\nu) - F_t((a-\mu)/\sigma;\,\nu)}, \quad x \in [a, b].

Value

dtrunct2 gives the density, ptrunct2 gives the distribution function, qtrunct2 gives the quantile function, and rtrunct2 generates random deviates.

Examples

x <- rtrunct2(1, df = 5, mu = 2, sigma = 3, min = -1, max = 5)
d <- dtrunct2(x, df = 5, mu = 2, sigma = 3, min = -1, max = 5)
p <- ptrunct2(x, df = 5, mu = 2, sigma = 3, min = -1, max = 5)
q <- qtrunct2(p, df = 5, mu = 2, sigma = 3, min = -1, max = 5)

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