cnorm {crch}R Documentation

The Censored Normal Distribution

Description

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

Usage

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

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

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

qcnorm(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 censored normal distribution has density f(x):

Φ((left - μ)/σ) if x ≤ left
1 - Φ((right - μ)/σ) if x ≥ right
φ((x - μ)/σ)/σ if left < x < right

where 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

dcnorm gives the density, pcnorm gives the distribution function, qcnorm gives the quantile function, and rcnorm generates random deviates.

See Also

dnorm


[Package crch version 1.0-2 Index]