# tlogis

##### The Truncated Logistic Distribution

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

- Keywords
- 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].

##### 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.

##### Value

`dtlogis`

gives the density, `ptlogis`

gives the distribution
function, `qtlogis`

gives the quantile function, and `rtlogis`

generates random deviates.

##### See Also

*Documentation reproduced from package crch, version 1.0-4, License: GPL-2 | GPL-3*