tlogis {crch}R Documentation

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].

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/σ λ((x - μ)/σ) / (Λ((right - μ)/σ) - Λ((left - μ)/σ))

for left ≤ x ≤ right, and 0 otherwise.

Λ and λ are the cumulative distribution function and probability density function of the standard logistic distribution respectively, μ is the location of the distribution, and σ 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


[Package crch version 1.0-2 Index]