

Generalized Extreme Value(rmutil)            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_:

     These functions provide information about the general-
     ized extreme value distribution with location parameter
     equal to `m', dispersion equal to `s', and family
     parameter equal to `f'.  `dgextval' gives the density,
     `pgextval' gives the distribution function, `hgextval'
     gives the hazard function.

     The generalized extreme value distribution has density

       f(y) = f y^(f-1) exp(y^f) (s/m) (exp(y^f)/m)^(s-1)
       exp(-(exp(y^f)/m)^s)/(1-I(f>0)+sign(f) exp(-m^-s))

     where m is the location parameter of the distribution,
     s is the dispersion, f is the family parameter, I() is
     the indicator function, and y>0.

     f=0 yields a Weibull distribution and f=1 a truncated
     extreme value distribution.  uthor{J.K. Lindsey}

_U_s_a_g_e_:

     dgextval(y, m, s, f)
     pgextval(q, m, s, f)
     hgextval(y, m, s, f)

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

       y: vector of responses.

       q: vector of quantiles.

       m: vector of location parameters.

       s: vector of dispersion parameters.

       f: vector of family parameters.

_A_u_t_h_o_r_(_s_)_:

     J.K. Lindsey

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

     `dweibull' for the Weibull distribution.

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

     dgextval(1, 2, 1, 2)
     pgextval(1, 2, 1, 2)

