gevUC                  package:VGAM                  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, distribution function, quantile function and random
     generation for the generalized extreme value distribution (GEV)
     with location parameter 'location', scale parameter 'scale' and
     shape parameter 'shape'.

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

     dgev(x, location=0, scale=1, shape=0)
     pgev(q, location=0, scale=1, shape=0)
     qgev(p, location=0, scale=1, shape=0)
     rgev(n, location=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. Positive integer of length 1.

location: the location parameter mu.

   scale: the scale parameter sigma. Must consist of positive values. 

   shape: the shape parameter xi.

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

     See 'gev', the 'VGAM' family function for estimating the two
     parameters by maximum likelihood estimation, for formulae and
     other details. Apart from 'n', all the above arguments may be
     vectors and are recyled to the appropriate length if necessary.

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

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

_N_o_t_e:

     The default value of xi=0 means the default distribution is the
     Gumbel.

     Currently, these functions have different argument names compared
     with those in the 'evd' package.

_A_u_t_h_o_r(_s):

     T. W. Yee

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

     Coles, S. (2001) _An Introduction to Statistical Modeling of
     Extreme Values_. London: Springer-Verlag.

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

     'gev'.

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

     ## Not run: 
     x = seq(-3, 3, by=0.01)
     loc = 0; sigma = 1; xi = -0.4
     plot(x, dgev(x, loc, sigma, xi), type="l", col="blue", ylim=c(0,1),
          main="Blue is density, red is cumulative distribution function",
          sub="Purple are 5,10,...,95 percentiles", ylab="", las=1)
     abline(h=0, col="blue", lty=2)
     lines(qgev(seq(0.05,0.95,by=0.05), loc, sigma, xi), 
           dgev(qgev(seq(0.05,0.95,by=0.05), loc, sigma, xi), loc, sigma, xi),
           col="purple", lty=3, type="h")
     lines(x, pgev(x, loc, sigma, xi), type="l", col="red")
     abline(h=0, lty=2)

     pgev(qgev(seq(0.05,0.95,by=0.05), loc, sigma, xi), loc, sigma, xi)
     ## End(Not run)

