KolmogorovDist            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 _K_o_l_m_o_g_o_r_o_v _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 Kolmogorov distance
     d_k of two distributions P and Q where the distributions are
     defined  on a finite-dimensional Euclidean space (R^m, B^m) with
     B^m the Borel-sigma-algebra on R^m. The Kolmogorov distance is
     defined as

 d_k(P,Q)=sup{|P({y in R^m | y <= x})-Q({y in R^m | y <= x})| | x in R^m}

     where <= is coordinatewise on R^m.

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

     KolmogorovDist(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

Kolmogorov.distance: Kolmogorov 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": Kolmogorov
          distance of two absolutely continuous  univariate
          distributions which is computed using a union of a
          (pseudo-)random and a deterministic grid.

     _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": Kolmogor
          ov distance of two discrete univariate distributions.  The
          distance is attained at some point of the union of the
          supports  of 'e1' and 'e2'.

     _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": Kolmogoro
          v distance of absolutely continuous and discrete univariate
          distributions. It is computed using a union of  a
          (pseudo-)random and a deterministic grid in combination with
          the support of 'e2'.

     _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": Kolmogoro
          v distance of discrete and absolutely continuous univariate
          distributions. It is computed using a union of  a
          (pseudo-)random and a deterministic grid in combination with
          the support of 'e1'.

_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.

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

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

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

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

     KolmogorovDist(Norm(), Gumbel())
     KolmogorovDist(Norm(), Td(10))
     KolmogorovDist(Norm(mean = 50, sd = sqrt(25)), Binom(size = 100))
     KolmogorovDist(Pois(10), Binom(size = 20)) 

