gpd                   package:evd                   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 location, scale and shape parameters.

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

     dgpd(x, loc=0, scale=1, shape=0, log = FALSE) 
     pgpd(q, loc=0, scale=1, shape=0, lower.tail = TRUE) 
     qgpd(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
     rgpd(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 generalized Pareto distribution function (Pickands, 1975) with
     parameters 'loc' = a, 'scale' = b and 'shape' = s is

                    G(z) = 1 - {1+s(z-a)/b}^(-1/s)

     for 1+s(z-a)/b > 0 and z > a, where b > 0. If s = 0 the
     distribution is defined by continuity.

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

     'dgpd' gives the density function, 'pgpd' gives the distribution
     function, 'qgpd' gives the quantile function, and 'rgpd' generates
     random deviates.

_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:

     'fpot', 'rgev'

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

     dgpd(2:4, 1, 0.5, 0.8)
     pgpd(2:4, 1, 0.5, 0.8)
     qgpd(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
     rgpd(6, 1, 0.5, 0.8)
     p <- (1:9)/10
     pgpd(qgpd(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

