

Logistic {base}                              R Documentation

_T_h_e _L_o_g_i_s_t_i_c _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_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_s_a_g_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_r_g_u_m_e_n_t_s_:

     x,q: vector of quantiles.

       p: vector of probabilities.

       n: number of observations to generate.

location,scale: location and scale parameters.

_D_e_t_a_i_l_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_x_a_m_p_l_e_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

