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.

See Also

dlogis