gumbel                  package:evd                  R Documentation

_T_h_e _G_u_m_b_e_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 function, distribution function, quantile function and
     random generation for the Gumbel distribution with location and
     scale parameters.

_U_s_a_g_e:

     dgumbel(x, loc=0, scale=1, log = FALSE) 
     pgumbel(q, loc=0, scale=1, lower.tail = TRUE) 
     qgumbel(p, loc=0, scale=1, lower.tail = TRUE)
     rgumbel(n, loc=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.

loc, scale: Location and scale parameters (can be given as vectors).

     log: Logical; if 'TRUE', the log density is returned.

lower.tail: Logical; if 'TRUE' (default), probabilities are P[X <= x],
          otherwise, P[X > x]

_D_e_t_a_i_l_s:

     The Gumbel distribution function with parameters 'loc' = a and
     'scale' = b is

                      G(x) = exp{-exp[-(z-a)/b]}

     for all real z, where b > 0.

_V_a_l_u_e:

     'dgumbel' gives the density function, 'pgumbel' gives the
     distribution function, 'qgumbel' gives the quantile function, and
     'rgumbel' generates random deviates.

_I_n_t_e_r_e_s_t_i_n_g _F_a_c_t:

     Gumbel is the name of my teddy bear. And a famous statistician.

_S_e_e _A_l_s_o:

     'rfrechet', 'rgev', 'rrweibull'

_E_x_a_m_p_l_e_s:

     dgumbel(-1:2, -1, 0.5)
     pgumbel(-1:2, -1, 0.5)
     qgumbel(seq(0.9, 0.6, -0.1), 2, 0.5)
     rgumbel(6, -1, 0.5)
     p <- (1:9)/10
     pgumbel(qgumbel(p, -1, 2), -1, 2)
     ## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

