pwm2lmom               package:lmomco               R Documentation

_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 _t_o _L-_m_o_m_e_n_t_s

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

     Converts the Probability-Weighted Moments (PWM) to the L-moments
     given the PWM. The conversion is linear so procedures based on
     PWMs and identical to  those based on L-moments.


                      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_0 mbox{,}


 lambda_5 = 70beta_4 - 140beta_3 + 90beta_2 - 20beta_1 + beta_0 mbox{,}


                   tau = lambda_2/lambda_1 mbox{,}


                  tau_3 = lambda_3/lambda_2 mbox{,}


                tau_4 = lambda_4/lambda_2 mbox{, and}


                  tau_5 = lambda_5/lambda_2 mbox{.}

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

     pwm2lmom(pwm)

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

     pwm: A PWM object created by 'pwm.ub' or similar. 

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

     The Probability Weighted Moments (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
     linearity between L-moments and Probability-Weighted Moments means
     that procedures base on one are equivalent to the other.

_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

_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', 'lmom2pwm'

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

     lmom <- pwm2lmom(pwm.ub(c(123,34,4,654,37,78)))

     pwm2lmom(pwm.ub(rnorm(100)))

