exi                   package:evd                   R Documentation

_E_s_t_i_m_a_t_e_s _o_f _t_h_e _E_x_t_r_e_m_a_l _I_n_d_e_x

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

     Estimates of the extremal index.

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

     exi(data, u, r = 1, ulow = rep(-Inf, ncol(u)), rlow =
         rep(1, length(r)), dimnames = list(NULL, NULL), drop = TRUE)

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

    data: A numeric vector, which may contain missing values.

       u: A numeric vector of thresholds, unless time varying
          thresholds are used, in which case 'u' should be a matrix,
          typically with 'length(data)' rows (or else the usual
          recycling rules are applied).

       r: A numeric vector of postive integers denoting the clustering
          interval lengths.

    ulow: A numeric vector of lower thresholds with length 'length(u)'
          (if 'u' is a vector) or 'ncol(u)' (if 'u' is a matrix),
          unless time varying lower thresholds are used, in which case
          'ulow' should be a matrix with 'length(u)' or 'ncol(u)'
          columns, and typically with 'length(data)' rows (or else the
          usual recycling rules are applied). By default there are no
          lower thresholds (or equivalently, the lower thresholds are
          '-Inf').

    rlow: A numeric vector of postive integers, of length 'length(r)',
          denoting the lower clustering interval lengths. The lower
          clustering interval length is only relevant if it is less
          than the clustering interval length and if there exists a
          lower threshold (greater than '-Inf').

dimnames: The 'dimnames' of the result.

    drop: Logical; return a vector if either 'u' or 'r' has one
          element/column?

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

     The extremal index is estimated using the inverse of the average
     cluster size, using the clusters of exceedences derived from
     'clusters'. If the threshold is larger than (or equal to)
     'max(data)', so that no clusters are derived, then the
     corresponding estimate is 'NaN'.

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

     A matrix with 'length(u)' (if 'u' is a vector) or 'ncol(u)' (if
     'u' is a matrix) rows and 'length(r)' columns, such that the
     'ij'th element is the estimate of the extremal index using the
     threshold 'u[i]' or 'u[,i]', the clustering interval length
     'r[j]', the lower threshold 'ulow[i]' or 'ulow[,i]', and the lower
     clustering interval length 'rlow[j]'. If 'drop' is 'TRUE' (the
     default), a numeric vector is returned in preference to a matrix
     with one row/column.

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

     'clusters'

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

     data(portpirie)
     exi(portpirie, 4.2, 3, 3.8)
     us <- seq(3.9, 4.2, len = 10)
     exi(portpirie, us, 3)
     exi(portpirie, us, 1:3)
     tvu <- c(rep(4.2, 20), rep(4.1, 25), rep(4.2, 20))
     exi(portpirie, as.matrix(tvu), 1:3)

     us <- seq(3.9, 4.2, len = 100)
     eis <- exi(portpirie, us, 1:3)
     matplot(us, eis, type = "l", xlab = "Threshold", ylab = "Ext. Index")

