extremalindex            package:extRemes            R Documentation

_E_s_t_i_m_a_t_e _t_h_e _e_x_t_r_e_m_a_l _i_n_d_e_x (_t_h_e_t_a)

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

     Estimates the extremal index based on the intervals estimator due
     to Ferro and Segers (2003).

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

     extremalindex(xdat, u)

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

    xdat: n X 1 numeric vector of the data. 

       u: User defined threshold.  May be a single number or a numeric
          n X 1 vector.

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

     The extremal index is a useful indicator of how much clustering of
     exceedances of a threshold occurs in the limit of the
     distribution.  If theta = 1, then the data is independent and if
     theta < 1, then there is some dependency (clustering) in the
     limit.

     There are many possible estimators of the extremal index.  The one
     used here is the intervals estimator described in Ferro and Segers
     (2003).  It is unbiased in the mean and can be used to estimate
     the number of clusters, which is also done by this function.

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

     A list with components: 

  theta : The intervals estimate of the extremal index (theta).

    msg : A message stating whether any interexceedance times were
          above 2 and possibly other pertinent information.

       C: The estimated number of clusters (handles ties).

run.length: The estimated run length for runs declustering.

_A_u_t_h_o_r(_s):

     Eric Gilleland

_R_e_f_e_r_e_n_c_e_s:

     Ferro, C.A.T. and Segers, J. (2003): Inference for clusters of
     extreme values, J.R. Statist. Soc. B, 65 (2): 545-556.

     Gilleland, Eric and Katz, Richard W. Tutorial for the 'Extremes
     Toolkit: Weather and Climate Applications of Extreme Value
     Statistics.' <URL: http://www.assessment.ucar.edu/toolkit>, 2005.

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

     'dclust'

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

     data( Tphap)
     temp <- -Tphap[,"MinT"]
     look <- extremalindex( temp, -70)
     look

     # See Gilleland et al. (2005) for more.

