lmomTLgpa               package:lmomco               R Documentation

_T_r_i_m_m_e_d _L-_m_o_m_e_n_t_s _o_f _t_h_e _G_e_n_e_r_a_l_i_z_e_d _P_a_r_e_t_o _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 symmetrical trimmed L-moments
     (TL-moments) for t=1 of the Generalized Pareto distribution given
     the parameters (xi, alpha, and kappa) from 'parTLgpa'. The
     TL-moments in terms of the parameters are


 lambda^{(1)}_1 = xi + frac{alpha(kappa+5)}{(kappa+3)(kappa+2)} mbox{,}


 lambda^{(1)}_2 = frac{6alpha}{(kappa+4)(kappa+3)(kappa+2)} mbox{,}


       tau^{(1)}_3 = frac{10(1-kappa)}{9(kappa+5)} mbox{, and}


 tau^{(1)}_4 = frac{5(kappa-1)(kappa-2)}{4(kappa+6)(kappa+5)}  mbox{.}

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

     lmomTLgpa(para)

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

    para: The parameters of the distribution.

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

     An R 'list' is returned.

 lambdas: Vector of the TL-moments. First element is lambda^{(1)}_1,
          second element is lambda^{(1)}_2, and so on.

  ratios: Vector of the L-moment ratios. Second element is  tau^{(1)},
          third element is tau^{(1)}_3 and so on. 

    trim: Trim level = 1

  source: An attribute identifying the computational source  of the
          TL-moments: "lmomTLgpa".

_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.

     Hosking, J.R.M., 1990, L-moments-Analysis and estimation of
     distributions using linear combinations of order statistics:
     Journal of the Royal Statistical Society, Series B, vol. 52, p.
     105-124.

     Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency
     analysis-An approach based on L-moments: Cambridge University
     Press.

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

     'parTLgpa', 'quagpa', 'cdfgpa'

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

     TL <- TLmoms(c(123,34,4,654,37,78,21,3400),trim=1)
     TL
     lmomTLgpa(parTLgpa(TL))

