tnorm {crch}R Documentation

The Truncated Normal Distribution

Description

Density, distribution function, quantile function, and random generation for the left and/or right truncated normal distribution.

Usage

dtnorm(x, mean = 0, sd = 1, left = -Inf, right = Inf, log = FALSE)

ptnorm(q, mean = 0, sd = 1, left = -Inf, right = Inf, 
  lower.tail = TRUE, log.p = FALSE)

rtnorm(n, mean = 0, sd = 1, left = -Inf, right = Inf)

qtnorm(p, mean = 0, sd = 1, left = -Inf, right = Inf, 
  lower.tail = TRUE, log.p = FALSE)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

mean

vector of means.

sd

vector of standard deviations.

left

left censoring point.

right

right censoring point.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].

Details

If mean or sd are not specified they assume the default values of 0 and 1, respectively. left and right have the defaults -Inf and Inf respectively.

The truncated normal distribution has density

f(x) = 1/σ φ((x - μ)/σ) / (Φ((right - μ)/σ) - Φ((left - μ)/σ))

for left ≤ x ≤ right, and 0 otherwise.

Φ and φ are the cumulative distribution function and probability density function of the standard normal distribution respectively, μ is the mean of the distribution, and σ the standard deviation.

Value

dtnorm gives the density, ptnorm gives the distribution function, qtnorm gives the quantile function, and rtnorm generates random deviates.

See Also

dnorm


[Package crch version 1.0-4 Index]