gpd                package:smoothtail                R Documentation

_T_h_e _G_e_n_e_r_a_l_i_z_e_d _P_a_r_e_t_o _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 Pareto distribution (GPD)
     with shape parameter gamma and  scale parameter sigma.

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

     dgpd(x, gam, sigma = 1) 
     pgpd(q, gam, sigma = 1) 
     qgpd(p, gam, sigma = 1)
     rgpd(n, gam, sigma = 1)

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

    x, q: Vector of quantiles.

       p: Vector of probabilities.

       n: Number of observations.

     gam: Shape parameter, real number.

   sigma: Scale parameter, positive real number.

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

     The generalized Pareto distribution function (Pickands, 1975) with
     shape parameter gamma and scale parameter sigma is


     W_{gamma,sigma}(x) = 1 - {(1+gamma x / sigma)}_+^{-1/gamma}.


     If gamma = 0, the distribution function is defined by continuity.
     The density is denoted by  w_{gamma, sigma}.

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

     'dgpd' gives the values of the density function, 'pgpd' those of
     the distribution function, and 'qgpd' those of the quantile
     function of the GPD at {bold x}, {bold q}, and {bold p}, 
     respectively. 'rgpd' generates n random numbers, returned as an
     ordered vector.

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

     Kaspar Rufibach, kaspar.rufibach@freesurf.ch, 
      <URL: http://www.stanford.edu/~kasparr> 

     Samuel Mueller, mueller@maths.uwa.edu.au, 
      <URL: http://www.maths.uwa.edu.au/Members/mueller>

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

     Pickands, J. (1975). Statistical inference using extreme order
     statistics.  _Annals of Statistics_, *3*, 119-131.

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

     Similar functions are provided in the R-packages 'evir' and 'evd'.

