Weibull                 package:base                 R Documentation

_T_h_e _W_e_i_b_u_l_l _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Density, distribution function, quantile function and random
     generation for the Weibull distribution with parameters `shape'
     and `scale'.

_U_s_a_g_e:

     dweibull(x, shape, scale = 1, log = FALSE)
     pweibull(q, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
     qweibull(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
     rweibull(n, shape, 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.

shape, scale: shape and scale parameters.

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].

_D_e_t_a_i_l_s:

     If `scale' is omitted it assumes the default value of `1'.

     The Weibull distribution with `shape' parameter a and `scale'
     parameter b has density given by

               f(x) = (a/b) (x/b)^(a-1) exp(- (x/b)^a)

     for x > 0.

_V_a_l_u_e:

     `dweibull' gives the density, `pweibull' gives the distribution
     function, `qweibull' gives the quantile function, and `rweibull'
     generates random deviates.

_N_o_t_e:

     The cumulative hazard H(t) = - log(1 - F(t)) is `-pweibull(t, r,
     lower = FALSE, log = TRUE)'.

_S_e_e _A_l_s_o:

     `dexp' for the Exponential which is a special case of a Weibull
     distribution.

_E_x_a_m_p_l_e_s:

     x <- 1:10
     all.equal(dweibull(x, shape = 1), dexp(x))
     all.equal(pweibull(x, shape = 1, scale = pi), pexp(x, rate = 1/pi))
     all.equal(qweibull(x/11, shape = 1, scale = pi), qexp(x/11, rate = 1/pi))

