varLmoments              package:nsRFA              R Documentation

_E_x_a_c_t _v_a_r_i_a_n_c_e _s_t_r_u_c_t_u_r_e _o_f _s_a_m_p_l_e _L-_m_o_m_e_n_t_s

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

     'varLmoments' provides distribution-free unbiased estimators of
     the variances and covariances of sample L-moments.

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

      varLmoments (x, matrix=TRUE)
      varLCV (x)
      varLCA (x)
      varLkur (x)

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

       x: vector representing a data-sample

  matrix: if 'TRUE' (default), the matrix of estimates of the variance
          structure (variance and covariance) i of sample L-moments is
          returned; if 'FALSE', a vector containing var(l1),  var(l2),
          var(l3), var(l4), var(t),  var(t3) and var(t4) is returned.

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

     The estimation of the exact variance structure of sample L-moments
     is based on Elamir et Seheult (2004).

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

     'varLmoments' gives the matrix of unbiased estimates of the
     variance structure of sample L-moments:  this is a 4x4 matrix
     containg var(l1), var(l2), var(l3),  var(l4) on the main diagonal,
      and the correspondant covariances elsewhere (cov(l1,l2),
     cov(l1,l3), etc.);

     'varLCV' gives the unbiased estimate of the variance of sample
     coefficient of L-variation of 'x';

     'varLCA' gives the unbiased estimate of the variance of sample
     L-skewness of 'x';

     'varLkur' gives the unbiased estimate of the variance of sample
     L-kurtosis of 'x'.

_N_o_t_e:

     For information on the package and the Author, and for all the
     references, see 'nsRFA'.

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

     'var', 'Lmoments'.

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

     x <- rnorm(30,10,2)
     varLmoments(x)
     varLmoments(x, FALSE)

     varLCV(x)
     varLCA(x)
     varLkur(x)

     data(hydroSIMN)
     x <- annualflows["dato"][,]
     cod <- annualflows["cod"][,]
     dvarLmom <- function(x) {diag(varLmoments(x))}
     sapply(split(x,cod),dvarLmom)

