Density, distribution function, quantile function, and random generation for the left and/or right truncated logistic distribution.
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)
dtlogis gives the density, ptlogis gives the distribution
function, qtlogis gives the quantile function, and rtlogis
generates random deviates.
vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length is
taken to be the number required.
location parameter.
scale parameter.
left truncation point.
right truncation point.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].
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.