gpdUC                  package:VGAM                  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, distribution function, quantile function and random
     generation for the generalized Pareto distribution (GPD) with
     location parameter 'location', scale parameter 'scale' and shape
     parameter 'shape'.

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

     dgpd(x, location=0, scale=1, shape=0)
     pgpd(q, location=0, scale=1, shape=0)
     qgpd(p, location=0, scale=1, shape=0)
     rgpd(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.

   shape: the shape parameter xi.

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

     See 'gpd', 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:

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

_N_o_t_e:

     The default values of all three parameters, especially xi=0, means
     the default distribution is the exponential.

     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:

     'gpd'.

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

     ## Not run: 
     x = seq(-0.2, 3, by=0.01)
     loc = 0; sigma = 1; xi = -0.4
     plot(x, dgpd(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(qgpd(seq(0.05,0.95,by=0.05), loc, sigma, xi), 
           dgpd(qgpd(seq(0.05,0.95,by=0.05), loc, sigma, xi), loc, sigma, xi),
           col="purple", lty=3, type="h")
     lines(x, pgpd(x, loc, sigma, xi), type="l", col="red")
     abline(h=0, lty=2)
     ## End(Not run)

