ksEstimator             package:ROptEst             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 _M_i_n_i_m_u_m _D_i_s_t_a_n_c_e _E_s_t_i_m_a_t_o_r

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

     Generic function for the computation of the Kolmogorov(-Smirnov)
     minimum distance estimator.

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

     ksEstimator(x, distribution, ...)

     ## S4 method for signature 'numeric, Binom':
     ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

     ## S4 method for signature 'numeric, Pois':
     ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

     ## S4 method for signature 'numeric, Norm':
     ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

     ## S4 method for signature 'numeric, Lnorm':
     ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

     ## S4 method for signature 'numeric, Gumbel':
     ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

     ## S4 method for signature 'numeric, Exp':
     ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

     ## S4 method for signature 'numeric, Gammad':
     ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

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

       x: sample 

distribution: object of class '"Distribution"' 

     ...: additional parameters 

   param: name of the unknown parameter. If missing all parameters of
          the corresponding distribution are estimated. 

     eps: the desired accuracy (convergence tolerance). 

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

     In case of discrete distributions the Kolmogorov distance is
     computed and the parameters which lead to the minimum distance are
     returned. In case of  absolutely continuous distributions
     'ks.test' is called and the parameters which minimize the
     corresponding test statistic are returned.

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

     The Kolmogorov minimum distance estimator is computed. Returns a
     list with components named like the parameters of 'distribution'.

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

     _x = "_n_u_m_e_r_i_c", _d_i_s_t_r_i_b_u_t_i_o_n = "_B_i_n_o_m" Binomial distributions. 

     _x = "_n_u_m_e_r_i_c", _d_i_s_t_r_i_b_u_t_i_o_n = "_P_o_i_s" Poisson distributions. 

     _x = "_n_u_m_e_r_i_c", _d_i_s_t_r_i_b_u_t_i_o_n = "_N_o_r_m" Normal distributions. 

     _x = "_n_u_m_e_r_i_c", _d_i_s_t_r_i_b_u_t_i_o_n = "_L_n_o_r_m" Lognormal distributions. 

     _x = "_n_u_m_e_r_i_c", _d_i_s_t_r_i_b_u_t_i_o_n = "_G_u_m_b_e_l" Gumbel distributions. 

     _x = "_n_u_m_e_r_i_c", _d_i_s_t_r_i_b_u_t_i_o_n = "_E_x_p" Exponential distributions. 

     _x = "_n_u_m_e_r_i_c", _d_i_s_t_r_i_b_u_t_i_o_n = "_G_a_m_m_a" Gamma distributions. 

_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.

     Kohl, M. (2005) _Numerical Contributions to the Asymptotic Theory
     of Robustness_.  Bayreuth: Dissertation.

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

     'Distribution-class'

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

     x <- rnorm(100, mean = 1, sd = 2)
     ksEstimator(x=x, distribution = Norm()) # estimate mean and sd
     ksEstimator(x=x, distribution = Norm(mean = 1), param = "sd") # estimate sd
     ksEstimator(x=x, distribution = Norm(sd = 2), param = "mean") # estimate mean
     mean(x)
     median(x)
     sd(x)
     mad(x)

