lmomgno                package:lmomco                R Documentation

_L-_m_o_m_e_n_t_s _o_f _t_h_e _G_e_n_e_r_a_l_i_z_e_d _N_o_r_m_a_l _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 L-moments of the Generalized Normal
     (log-Normal) distribution given the parameters (xi, alpha, and
     kappa) from 'pargno'. The L-moments in terms of the parameters are


    lambda_1 = xi + frac{alpha}{kappa}(1-e^{kappa^2/2}) mbox{ and}


 lambda_2 = frac{alpha}{kappa}(e^{kappa^2/2})(1-2Phi(-kappa/sqrt{2})) mbox{,}


     where Phi is the cumulative distribution of the standard normal
     distribution. There are no simple expressions for tau_3, tau_4,
     and tau_5. Log transformation of the data prior to fitting of the 
     Generalized Normal distribution is not required.

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

     lmomgno(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.

      L1: Arithmetic mean.

      L2: L-scale-analogous to standard deviation.

     LCV: coefficient of L-variation-analogous to coe. of variation.

    TAU3: The third L-moment ratio or L-skew-analogous to skew.

    TAU4: The fourth L-moment ratio or L-kurtosis-analogous to
          kurtosis.

    TAU5: The fifth L-moment ratio.

      L3: The third L-moment.

      L4: The fourth L-moment.

      L5: The fifth L-moment.

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

_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.

     Hosking, J.R.M., 1996, FORTRAN routines for use with the method of
     L-moments: Version 3, IBM Research Report RC20525, T.J. Watson
     Research Center, Yorktown Heights, New York.

     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:

     'pargno', 'quagno', 'cdfgno'

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

     lmr <- lmom.ub(c(123,34,4,654,37,78))
     lmr
     lmomgno(pargno(lmr))

