gev                   package:evd                   R Documentation

_T_h_e _G_e_n_e_r_a_l_i_z_e_d _E_x_t_r_e_m_e _V_a_l_u_e _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 generalized extreme value (GEV)
     distribution with location, scale and shape parameters.

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

     dgev(x, loc=0, scale=1, shape=0, log = FALSE) 
     pgev(q, loc=0, scale=1, shape=0, lower.tail = TRUE) 
     qgev(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
     rgev(n, loc=0, scale=1, shape=0)

_A_r_g_u_m_e_n_t_s:

    x, q: Vector of quantiles.

       p: Vector of probabilities.

       n: Number of observations.

loc, scale, shape: Location, scale and shape parameters; the  'shape'
          argument cannot be a vector (must have length one).

     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 GEV distribution function with parameters 'loc' = a, 'scale' =
     b and 'shape' = s is

                   G(x) = exp[-{1+s(z-a)/b}^(-1/s)]

     for 1+s(z-a)/b > 0, where b > 0. If s = 0 the distribution is
     defined by continuity. If 1+s(z-a)/b <= 0, the value z is either
     greater than the upper end point (if s < 0), or less than the
     lower end point (if s > 0).

     The parametric form of the GEV encompasses that of the Gumbel,
     Frechet and reversed Weibull distributions, which are obtained for
     s = 0, s > 0 and s < 0 respectively. It was first introduced by
     Jenkinson (1955).

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

     'dgev' gives the density function, 'pgev' gives the distribution
     function, 'qgev' gives the quantile function, and 'rgev' generates
     random deviates.

_R_e_f_e_r_e_n_c_e_s:

     Jenkinson, A. F. (1955) The frequency distribution of the annual
     maximum (or minimum) of meteorological elements. _Quart. J. R.
     Met. Soc._, *81*, 158-171.

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

     'fgev', 'rfrechet', 'rgumbel', 'rrweibull'

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

     dgev(2:4, 1, 0.5, 0.8)
     pgev(2:4, 1, 0.5, 0.8)
     qgev(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
     rgev(6, 1, 0.5, 0.8)
     p <- (1:9)/10
     pgev(qgev(p, 1, 2, 0.8), 1, 2, 0.8)
     ## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

