lmom2pwm               package:lmomco               R Documentation

_L-_m_o_m_e_n_t_s _t_o _P_r_o_b_a_b_i_l_i_t_y-_W_e_i_g_h_t_e_d _M_o_m_e_n_t_s

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

     Converts the L-moments to the Probability-Weighted Moments (PWMs)
     given the L-moments. The conversion is linear so procedures based
     on  L-moments are identical to those based on PWMs. The relation
     between L-moments and PWMs is shown with 'pwm2lmom'.

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

     lmom2pwm(lmom)

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

    lmom: An L-moment object created by 'lmom.ub' or similar.

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

     PWMs are linear combinations of the L-moments and therefore
     contain the same statistical information of the data as the
     L-moments. However, the PWMs are harder to interpret as measures
     of probability distributions. The PWMs are included here for
     theoretical completeness and are not intended for use with the
     majority of the other functions implementing the various
     probability distributions. The relation between L-moments
     (lambda_r)and PWMs (beta_{r-1}) for 1 <= r <= 5 order is


                      lambda_1 = beta_0 mbox{,}



                 lambda_2 = 2beta_1 - beta_0 mbox{,}



            lambda_3 = 6beta_2 - 6beta_1 + beta_0 mbox{,}



    lambda_4 = 20beta_3 - 30beta_2 + 12beta_1 - beta_0mbox{, and}



 lambda_5 = 70beta_4  - 140beta_3 + 90beta_2 - 20beta_1 + beta_0mbox{.}


     The linearity between L-moments and PWMs means that procedures
     based on one are equivalent to the other.

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

     An R 'list' is returned.

   BETA0: The first PWM-equal to the arithmetic mean.

   BETA1: The second PWM.

   BETA2: The third PWM.

   BETA3: The fourth PWM.

   BETA4: The fifth PWM.

_A_u_t_h_o_r(_s):

     W.H. Asquith

_R_e_f_e_r_e_n_c_e_s:

     Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, J.R.,
     1979, Probability weighted moments-Definition and relation to
     parameters of several distributions expressable in inverse form:
     Water Resources Research, vol. 15, p. 1,049-1,054.

     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:

     'lmom.ub', 'pwm.ub', 'pwm2lmom'

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

     pwm <- lmom2pwm(lmom.ub(c(123,34,4,654,37,78)))

     lmom2pwm(lmom.ub(rnorm(100)))

