

   Logistic {base}                              R Documentation

   TThhee LLooggiissttiicc DDiissttrriibbuuttiioonn

   DDeessccrriippttiioonn::

        These functions provide information about the logistic
        distribution with parameters `location' and `scale'.
        `dlogis' gives the density, `plogis' gives the distri-
        bution function `qlogis' gives the quantile function
        and `rlogis' generates random deviates.

   UUssaaggee::

        dlogis(x, location=0, scale=1)
        plogis(q, location=0, scale=1)
        qlogis(p, location=0, scale=1)
        rlogis(n, location=0, scale=1)

   AArrgguummeennttss::

        x,q: vector of quantiles.

          p: vector of probabilities.

          n: number of observations to generate.

   location,scale: location and scale parameters.

   DDeettaaiillss::

        If `location' or `scale' are omitted, they assume the
        default values of `0' and `1' respectively.

        The Logistic distribution with `location' = m and
        `scale' = s has distribution function

                    F(x) = 1 / (1 + exp(-(x-m)/s))

        and density

            f(x) = 1/s exp((x-m)/s) (1 + exp((x-m)/s))^-2.

        It is a long-tailed distribution with mean m and vari-
        ance pi^2 /3 s^2.

   EExxaammpplleess::

        eps <- 100 * .Machine$double.eps
        x <- c(0:4, rlogis(100))
        all.equal(plogis(x, loc = 0), 1/(1 + exp(-x)),          tol = eps)
        all.equal(dlogis(x, loc = 0), exp(x) * (1 + exp(x))^-2, tol = eps)

        var(rlogis(4000, 0, s = 5))# approximately (+/- 3)
        pi^2/3 * 5^2

