crch (version 1.0-4)

# tlogis: The Truncated Logistic Distribution

## Description

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

## Usage

dtlogis(x, location = 0, scale = 1, left = -Inf, right = Inf, log = FALSE)ptlogis(q, location = 0, scale = 1, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)rtlogis(n, location = 0, scale = 1, left = -Inf, right = Inf)qtlogis(p, location = 0, scale = 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.

location

location parameter.

scale

scale parameter.

left

left truncation point.

right

right truncation 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].

## Value

dtlogis gives the density, ptlogis gives the distribution function, qtlogis gives the quantile function, and rtlogis generates random deviates.

## Details

If location or scale 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 logistic distribution has density

$$f(x) = 1/\sigma \lambda((x - \mu)/\sigma) / (\Lambda((right - \mu)/\sigma) - \Lambda((left - \mu)/\sigma))$$ for $$left \le x \le right$$, and 0 otherwise.

$$\Lambda$$ and $$\lambda$$ are the cumulative distribution function and probability density function of the standard logistic distribution respectively, $$\mu$$ is the location of the distribution, and $$\sigma$$ the scale.

dlogis