lmomgum                package:lmomco                R Documentation

_L-_m_o_m_e_n_t_s _o_f _t_h_e _G_u_m_b_e_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 Gumbel distribution
     given the parameters (xi and alpha) from 'pargum'. The L-moments
     in terms of the parameters are


              lambda_1 = xi + (0.5722...) alpha mbox{,}


                   lambda_2 = alpha log(2) mbox{,}


                       tau_3 = 0.169925 mbox{,}


                     tau_4 = 0.150375 mbox{, and}


                       tau_5 = 0.055868 mbox{.}

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

     lmomgum(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: "lmomgum".

_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:

     'pargum', 'quagum', 'cdfgum'

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

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

