extreme value           package:smoothSurv           R Documentation

_D_e_n_s_i_t_y _o_f _t_h_e _E_x_t_r_e_m_e _V_a_l_u_e _D_i_s_t_r_i_b_u_t_i_o_n _o_f _a _M_i_n_i_m_u_m.

_D_e_s_c_r_i_p_t_i_o_n:

     Density function of the extreme value distribution of a minimum
     with location alpha and scale beta and the density of the
     standardized version (with zero mean and unit variance).

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

     dextreme(x, alpha=0, beta=1)
     dstextreme(x)

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

       x: Vector of quantiles. 

   alpha: Vector of location parameters. 

    beta: Vector of scale parameters. 

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

     Extreme value distribution of a minimum with the location alpha
     and the scale beta has a density

      f(x) = (1/beta)*exp((x-alpha)/beta - exp((x-alpha)/beta))

     the mean equal to alpha - beta*e, where e is approximately 0.5772
     and the variance equal to beta^2 pi^2/6. Its standardized version
     is obtained with alpha = (sqrt(6)/pi)*e  and beta = (sqrt(6)/pi).

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

     The value of the density.

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

     Arno&#353t Kom&#225rek komarek@karlin.mff.cuni.cz

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

     dextreme(1, (sqrt(6)/pi)*0.5772, sqrt(6)/pi)
     dstextreme(1)        ## approximately same result as on the previous row

