TLmoms                package:lmomco                R Documentation

_T_h_e _S_a_m_p_l_e _T_r_i_m_m_e_d _L-_m_o_m_e_n_t_s _a_n_d _L-_m_o_m_e_n_t _R_a_t_i_o_s

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

     Compute the sample trimmed L-moments (TL-moments) for a vector.
     The level of symmetrical trimming is specified. A TL-moment is 


 hat{lambda}^{(t_1,t_2)}_r = frac{1}{r}sum^{n-t_2}_{i=t_1+1} <=ft[ frac{sumlimits^{r-1}_{k=0}{ (-1)^k {r-1 choose k} {i-1 choose r+t_1-1-k} {n-i choose t_2+k} }}{{n choose r+t_1+t_2}} right] x_{i:n} mbox{,}


     where t represents the trimming level of the t-largest or
     t-smallest  values, r represents the order of the L-moments, n
     represents the  sample size, and x_{i:n} represents the ith sample
     order statistic (x_{1:n} <= x_{2:n} <= ... <= x_{n:n}). This
     function loops across the above equation for each 'nmom' set in 
     the argument list.

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

     TLmoms(x,nmom,trim=NULL,leftrim=NULL,rightrim=NULL)

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

       x: A vector of data values.

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

    trim: Level of symmetrical trimming to use in the computations,
          which will equal 'NULL' if asymmetrical trimming was used.
          Although 'NULL' in the argument list, the default is 0-the
          usual L-moment is returned.

 leftrim: Level of trimming of the left-tail of the sample.

rightrim: Level of trimming of the right-tail of the sample.

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

     An R 'list' is returned.

 lambdas: Vector of the TL-moments. First element is
          hat{lambda}^{(t_1,t_2)}_1, second element is
          hat{lambda}^{(t_1,t_2)}_2, and so on.

  ratios: Vector of the L-moment ratios. Second element is 
          hat{tau}^{(t_1,t_2)}, third element is hat{tau}^{(t_1,t_2)}_3
          and so on.

    trim: Level of symmetrical trimming used in the computation, which
          will equal 'NULL' if asymmetrical trimming was used.

 leftrim: Level of left-tail trimming used in the computation.

rightrim: Level of right-tail trimming used in the computation.

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

_N_o_t_e:

     It is important to note that the "L-moment object" returned by
     'TLmoms' is different in structure to that returned by 'lmom.ub',
     'pwm2lmom', and similar as the TL-moments should not be confused
     with the ordinary L-moments. Implementation in the package might
     change.

_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.

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

     'TLmom', 'lmoms', and 'lmorph'

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

     X1 <- rcauchy(30)
     TL <- TLmoms(X1,nmom=6,trim=1)

