atvnonpar                package:evd                R Documentation

_N_o_n-_p_a_r_a_m_e_t_r_i_c _E_s_t_i_m_a_t_e_s _f_o_r _D_e_p_e_n_d_e_n_c_e _F_u_n_c_t_i_o_n_s _o_f _t_h_e
_T_r_i_v_a_r_i_a_t_e _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:

     Calculate or plot non-parametric estimates for the dependence
     function A of the trivariate extreme value distribution.

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

     atvnonpar(x = rep(1/3,3), data, nsloc1 = NULL, nsloc2 = NULL, nsloc3 = NULL,
         method = c("pickands", "deheuvels", "hall"), plot = FALSE,
         col = heat.colors(12), blty = 0, grid = if(blty) 150 else 50,
         lower = 1/3, ord = 1:3, lab = as.character(1:3), lcex = 1)

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

       x: A vector of length three or a matrix with three columns, in
          which case the dependence function is evaluated across the
          rows (ignored if plot is 'TRUE'). The elements/rows of the
          vector/matrix should be positive and should sum to one, or
          else they should have a positive sum, in which case the rows
          are rescaled and a warning is given. A(1/3,1/3,1/3) is
          returned by default since it is often a useful summary of
          dependence.

    data: A matrix or data frame with three columns, which may contain
          missing values.

nsloc1, nsloc2, nsloc3: A data frame with the same number of rows as
          'data', for linear modelling of the location parameter on the
          first/second/third margin. The data frames are treated as
          covariate matrices, excluding the intercept. A numeric vector
          can be given as an alternative to a single column data frame.

  method: The estimation method; a character string. Must be either
          '"pickands"' (the default), '"deheuvels"' or '"hall"' (or any
          unique partial match). The three estimators are very similar,
          and may not be distinguishable when plotted.

    plot: Logical; if 'TRUE' the function is plotted. The minimum
          (evaluated) value is returned invisibly. If 'FALSE' (the
          default), the following arguments are ignored.

     col: A list of colours (see 'image'). The first colours in the
          list represent smaller values, and hence stronger dependence.
          Each colour represents an equally spaced interval between
          'lower' and one.

    blty: The border line type, for the border that surrounds the
          triangular image. By default 'blty' is zero, so no border is
          plotted. Plotting a border leads to (by default) an increase
          in 'grid' (and hence computation time), to ensure that the
          image fits within it.

    grid: For plotting, the function is evaluated at 'grid^2' points.

   lower: The minimum value for which colours are plotted. By default
          'lower' = 1/3 as this is the theoretical minimum of the
          dependence function of the trivariate extreme value
          distribution.

     ord: A vector of length three, which should be a permutation of
          the set {1,2,3}. The points (1,0,0), (0,1,0) and (0,0,1) (the
          vertices of the simplex) are depicted clockwise from the top
          in the order defined by 'ord'.

     lab: A character vector of length three, in which case the 'i'th
          margin is labelled using the 'i'th component, or 'NULL', in
          which case no labels are given. By default, 'lab' is
          'as.character(1:3)'. The actual location of the margins, and
          hence the labels, is defined by 'ord'.

    lcex: A numerical value giving the amount by which the labels
          should be scaled relative to the default. Ignored if 'lab' is
          'NULL'.

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

     'atvnonpar' calculates or plots a non-parametric estimate of the
     dependence function of the trivariate extreme value distribution.

_N_o_t_e:

     The rows of 'data' that contain missing values are not used in the
     estimation of the dependence structure, but every non-missing
     value is used in estimating the generalized extreme value margins.

     The dependence function of the trivariate extreme value
     distribution is defined in 'atvpar'. The function 'atvpar'
     calculates and plots dependence functions of trivariate logistic
     and trivariate asymmetric logistic models.

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

     'atvpar', 'abvnonpar', 'fgev'

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

     s3pts <- matrix(rexp(30), nrow = 10, ncol = 3)
     s3pts <- s3pts/rowSums(s3pts)
     sdat <- rmvevd(100, dep = 0.6, model = "log", d = 3)
     atvnonpar(s3pts, sdat)

     ## Not run: atvnonpar(data = sdat, plot = TRUE)
     ## Not run: atvnonpar(data = sdat, plot = TRUE, ord = c(2,3,1), lab = LETTERS[1:3])
     ## Not run: atvpar(dep = 0.6, model = "log", plot = TRUE)
     ## Not run: atvpar(dep = 0.6, model = "log", plot = TRUE, blty = 1)

