parcau                package:lmomco                R Documentation

_E_s_t_i_m_a_t_e _t_h_e _P_a_r_a_m_e_t_e_r_s _o_f _t_h_e _C_a_u_c_h_y _D_i_s_t_r_i_b_u_t_i_o_n

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

     This function estimates the parameters of the Cauchy distribution
     from the trimmed L-moments (TL-moments) having trim level 1.

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

     parcau(lmom)

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

    lmom: TL-moments from 'TLmoms' with 'trim=1'.

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

     Unlike many of the other distributions in this package, the
     parameter estimation occurs by passing the data into the function
     and not from passing of an L-moment object (see 'lmom.ub').
     Contrast this practice with 'pargum' for example.) The reason this
     is so is because the usual L-moments are undefined for the Cauchy
     distribution, but the trimmed L-moments with a symmetrical
     trimming parameter are defined. Specifically, the L-moments by
     trimming the smallest and largest order statistic expections of
     the Cauchy are defined by Elamir and Seheult (2003). The function
     'parcau' calls 'TLlmoms(x,trim=1)') internally to compute the
     trimmed L-moments. The relation between the parameters and the
     trimmed L-moments is


                    xi = lambda^{(1)}_1 mbox{and}



             alpha = frac{lambda^{(1)}_2}{0.698} mbox{.}

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

     An R 'list' is returned.

    type: The type of distribution: 'cau'.

    para: The parameters of the distribution.

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

     W.H. Asquith

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

     Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments:
     Computational Statistics and Data Analysis, vol. 43, pp. 299-314.

     Gilchrist, W.G., 2000, Statistical modeling with quantile
     functions:  Chapman and Hall/CRC, Boca Raton, FL.

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

     'TLmoms', 'lmomcau'

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

     X1 <- rcauchy(20)
     parcau(TLmoms(X1,trim=1))

