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)

qtlogis(p, location = 0, scale = 1, left = -Inf, right = Inf, 
  lower.tail = TRUE, log.p = FALSE)

rtlogis(n, location = 0, scale = 1, left = -Inf, right = Inf)

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

$f(x)=1/\sigma \lambda ((x-\mu )/\sigma )/(\mathrm{\Lambda }((right-\mu )/\sigma )-\mathrm{\Lambda }((left-\mu )/\sigma ))$

for $left\le x\le right$, and 0 otherwise.

$\mathrm{\Lambda }$ 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

dlogis