TLmom                 package:lmomco                 R Documentation

_A _S_a_m_p_l_e _T_r_i_m_m_e_d _L-_m_o_m_e_n_t

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

     A sample trimmed L-moment (TL-moment) is computed for a vector.
     The r >= 1 order of the L-moment is specified as well as the level
     of symmetrical trimming.  A trimmed TL-moment is 


 hat{lambda}^{(t)}_r = frac{1}{r}sum^{n-t}_{i=t+1} <=ft[ frac{sumlimits^{r-1}_{k=0}{ (-1)^k {r-1 choose k} {i-1 choose r+t-1-k} {n-i choose t+k} }}{{n choose r+2t}} 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}).

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

     TLmom(x,order,trim=NULL,leftrim=NULL,rightrim=NULL,sortdata)

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

       x: A vector of data values.

   order: L-moment order to use in the computations.  Default is 1 (the
          mean).

    trim: Level of symmetrical trimming to use in the computations. 
          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.

sortdata: A logical switch on whether the data should be sorted. The
          default is TRUE.

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

     An R 'list' is returned.

  lambda: The TL-moment of order='order' and trimming='trim'.

   order: L-moment order computed. Default is 1 (the mean).

    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.

_N_o_t_e:

     The presence of the 'sortdata' switch can be dangerous. L-moment 
     computation requires that the data be sorted into the "order
     statistics". Thus the default behavior of 'sortdata=TRUE' is
     required when the function is called on its own. In practice, this
     function would not be used as multiple trimmed L-moments would be
     needed. Multiple trimmed L-moments are best computed by 'TLmoms',
     which calls 'TLmom' multiple times. The function 'TLmoms' takes
     over the sort operation on the data and passes 'sortdata=FALSE' to
     'TLmom' for efficiency. (The point of this discussion is that one
     does not want to waste CPU time sorting the data more than once.)

_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:

     'TLmoms'

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

     X1 <- rcauchy(30)
     TL <- TLmom(X1,order=2,trim=1)

