theoLmoms               package:lmomco               R Documentation

_T_h_e _T_h_e_o_r_e_t_i_c_a_l _L-_m_o_m_e_n_t_s _a_n_d _L-_m_o_m_e_n_t _R_a_t_i_o_s _u_s_i_n_g _I_n_t_e_g_r_a_t_i_o_n _o_f _t_h_e _Q_u_a_n_t_i_l_e _F_u_n_c_t_i_o_n

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

     Compute the theoretrical L-moments for a vector. A theoretrical
     L-moment in integral form is 


 lambda_r = frac{1}{r} sum^{r-1}_{k=0}{(-1)^k {r-1 choose k} frac{r!:I_r}{(r-k-1)!k!}  } mbox{, in which }



    I_r = int^1_0 X(F) times F^{r-k-1}(1-F)^{k},mathrm{d}F mbox{,}


     where X(F) is the quantile function of the random variable X for
     nonexceedance probability F, and r represents the order of the
     L-moments. This function actually dispatches to 'theoTLmoms' with
     'trim=0' argument.

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

     theoLmoms(para,nmom=5,verbose=FALSE)

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

    para: A distribution parameter object of this package 'vec2par'.

    nmom: The number of moments to compute. Default is 5.

 verbose: Toggle verbose output. Because the R function 'integrate' is
          used to perform the numerical integration, it might be useful
          to see selected messages regarding the numerical integration.

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

     An R 'list' is returned.

 lambdas: Vector of the TL-moments. First element is lambda_1, second
          element is lambda_2, and so on.

  ratios: Vector of the L-moment ratios. Second element is  tau_2,
          third element is tau_3 and so on.

    trim: Level of symmetrical trimming used in the computation, which
          will equal zero (the ordinary L-moments).

  source: An attribute identifying the computational source of the
          L-moments: "theoTLmoms".

_N_o_t_e:

     The actual function used is
     'theoLmoms(para,nmom=nmom,trim=0,verbose=verbose'.

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

     W.H. Asquith

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

     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.

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

     'theoTLmoms', 'par2qua', 'TLmoms', 'lmom.ub'

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

     para <- vec2par(c(0,1),type='nor') # standard normal
     TL00 <- theoLmoms(para) # compute ordinary L-moments

