TotalVarDist             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 _t_o_t_a_l _v_a_r_i_a_t_i_o_n _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 total variation
     distance d_v of two distributions P and Q where the distributions
     may be  defined for an arbitrary sample space (Omega, A). The
     total variation distance is defined as

                  d_v(P,Q)=sup{|P(B)-Q(B)| | B in A}

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

     TotalVarDist(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

total.variation.distance: total variation 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": total
          variation 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": total
          variation 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": total
          variation 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": total
          variation 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:

     Huber, P.J. (1981) _Robust Statistics_. New York: Wiley.

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

     'TotalVarDist-methods', 'ContaminationSize',  'KolmogorovDist',
     'HellingerDist',  'Distribution-class'

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

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

