abvpar                  package:evd                  R Documentation

_P_a_r_a_m_e_t_r_i_c _D_e_p_e_n_d_e_n_c_e _F_u_n_c_t_i_o_n_s _o_f _B_i_v_a_r_i_a_t_e _E_x_t_r_e_m_e
_V_a_l_u_e _M_o_d_e_l_s

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

     Calculate or plot the dependence function A for eight parametric
     bivariate extreme value models.

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

     abvpar(x = 0.5, dep, asy = c(1,1), alpha, beta, model = "log",
          plot = FALSE, add = FALSE, lty = 1, lwd = 1, col = 1, blty = 3,
          xlim = c(0,1), ylim = c(0.5,1), xlab = "", ylab = "", ...)

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

       x: A vector of values at which the dependence function is
          evaluated (ignored if plot or add is 'TRUE'). A(1/2) is
          returned by default since it is often a useful summary of
          dependence.

     dep: Dependence parameter for the logistic, asymmetric logistic,
          Husler-Reiss, negative logistic and asymmetric negative
          logistic models.

     asy: A vector of length two, containing the two asymmetry
          parameters for the asymmetric logistic and asymmetric
          negative logistic models.

alpha, beta: Alpha and beta parameters for the bilogistic, negative
          bilogistic and Coles-Tawn models.

   model: The specified model; a character string. Must be either
          '"log"' (the default), '"alog"', '"hr"', '"neglog"',
          '"aneglog"', '"bilog"', '"negbilog"' or '"ct"' (or any unique
          partial match), for the logistic, asymmetric logistic,
          Husler-Reiss, negative logistic, asymmetric negative
          logistic, bilogistic, negative bilogistic and Coles-Tawn
          models respectively. The definition of each model is given in
          'rbvevd'. If parameter arguments are given that do not
          correspond to the specified model those arguments are
          ignored, with a warning.

    plot: Logical; if 'TRUE' the function is plotted. The x and y
          values used to create the plot are returned invisibly. If
          'plot' and 'add' are 'FALSE' (the default), the arguments
          following 'add' are ignored.

     add: Logical; add to an existing plot? The existing plot should
          have been created using either 'abvpar' or 'abvnonpar', the
          latter of which plots (or calculates) a non-parametric
          estimate of the dependence function.

lty, blty: Function and border line types. Set 'blty' to zero to omit
          the border.

     lwd: Line width.

     col: Line colour.

xlim, ylim: x and y-axis limits.

xlab, ylab: x and y-axis labels.

     ...: Other high-level graphics parameters to be passed to 'plot'.

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

     Any bivariate extreme value distribution can be written as

                G(z1,z2) = exp{-(y1+y2)A[y1/(y1+y2)]}

     for some function A() defined on [0,1], where    

                    yi = {1+si(zi-ai)/bi}^(-1/si)

     for 1+si(zi-ai)/bi > 0 and i = 1,2, with the (generalized extreme
     value) marginal parameters given by (ai,bi,si), bi > 0. If si = 0
     then yi is defined by continuity.

     A() is called (by some authors) the dependence function. It
     follows that A(0)=A(1)=1, and that A() is a convex function with
     max(x,1-x) <= A(x) <= 1 for all 0 <= x <= 1. The lower and upper
     limits of A are obtained under complete dependence and
     independence respectively. A() does not depend on the marginal
     parameters.

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

     'abvpar' calculates or plots the dependence function for one of
     eight parametric bivariate extreme value models, at specified
     parameter values.

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

     'abvnonpar', 'fbvevd', 'rbvevd', 'atvpar'

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

     abvpar(dep = 2.7, model = "hr")
     abvpar(seq(0,1,0.25), dep = 0.3, asy = c(.7,.9), model = "alog")
     abvpar(alpha = 0.3, beta = 1.2, model = "negbi", plot = TRUE)

     bvdata <- rbvevd(100, dep = 0.7, model = "log")
     M1 <- fitted(fbvevd(bvdata, model = "log"))
     abvpar(dep = M1["dep"], model = "log", plot = TRUE)
     abvnonpar(data = bvdata, add = TRUE, lty = 2)

