HellingerDist            package:distrEx            R Documentation

_G_e_n_e_r_i_c _f_u_n_c_t_i_o_n _f_o_r _t_h_e _c_o_m_p_u_t_a_t_i_o_n _o_f _t_h_e _H_e_l_l_i_n_g_e_r _d_i_s_t_a_n_c_e _o_f _t_w_o _d_i_s_t_r_i_b_u_t_i_o_n_s

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

     Generic function for the computation of the Hellinger distance d_h
     of two distributions P and Q which may be defined for an arbitrary
      sample space (Omega, A). The Hellinger distance is defined as

                    0.5 int |sqrt{dP}-sqrt{dQ}|^2

     where sqrt{dP}, respectively sqrt{dQ} denotes the square root  of
     the densities.

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

     HellingerDist(e1, e2)

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

      e1: object of class '"Distribution"' 

      e2: object of class '"Distribution"' 

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

     A list containing the following components: 

      e1: object of class '"Distribution"'; distribution 1  

      e2: object of class '"Distribution"'; distribution 2

Hellinger.distance: Hellinger distance of 'e1' and 'e2'

_M_e_t_h_o_d_s:

     _e_1 = "_A_b_s_c_o_n_t_D_i_s_t_r_i_b_u_t_i_o_n", _e_2 = "_A_b_s_c_o_n_t_D_i_s_t_r_i_b_u_t_i_o_n": Hellinger
          distance of two absolutely continuous  univariate
          distributions which is computed using 'distrExintegrate'.


     _e_1 = "_A_b_s_c_o_n_t_D_i_s_t_r_i_b_u_t_i_o_n", _e_2 = "_D_i_s_c_r_e_t_e_D_i_s_t_r_i_b_u_t_i_o_n": Hellinger
          distance of absolutely continuous and discrete univariate
          distributions (are mutually singular; i.e.,  have distance
          '=1').

     _e_1 = "_D_i_s_c_r_e_t_e_D_i_s_t_r_i_b_u_t_i_o_n", _e_2 = "_D_i_s_c_r_e_t_e_D_i_s_t_r_i_b_u_t_i_o_n": Hellinge
          r distance of two discrete univariate distributions which is
          computed using 'support' and 'sum'.


     _e_1 = "_D_i_s_c_r_e_t_e_D_i_s_t_r_i_b_u_t_i_o_n", _e_2 = "_A_b_s_c_o_n_t_D_i_s_t_r_i_b_u_t_i_o_n": 
          Hellinger distance of discrete and absolutely continuous 
          univariate distributions (are mutually singular; i.e.,  have
          distance '=1').

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

     Matthias Kohl Matthias.Kohl@stamats.de

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

     Rieder, H. (1994) _Robust Asymptotic Statistics_. New York:
     Springer.

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

     'distrExIntegrate', 'ContaminationSize',  'TotalVarDist',
     'KolmogorovDist',  'Distribution-class'

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

     HellingerDist(Norm(), Gumbel())
     HellingerDist(Norm(), Td(10))
     HellingerDist(Norm(mean = 50, sd = sqrt(25)), Binom(size = 100)) # mutually singular
     HellingerDist(Pois(10), Binom(size = 20)) 

