parnor                package:lmomco                R Documentation

_E_s_t_i_m_a_t_e _t_h_e _P_a_r_a_m_e_t_e_r_s _o_f _t_h_e _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 parameters of the Normal distribution
     given the L-moments of the data in an L-moment object such as that
     returned by 'lmom.ub'. The relation between distribution
     parameters and L-moments is seen under 'lmomnor'. There are
     interesting parallels between lambda_2 (L-scale) and sigma
     (standard deviation). The sigma estimated from this function will
     not necessarily equal the output of the 'sd()' function of R. See
     the extended example for further illustration.

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

     parnor(lmom)

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

    lmom: A L-moment object created by 'lmom.ub' or 'pwm2lmom'.

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

     An R 'list' is returned.

    type: The type of distribution: 'nor'.

    para: The parameters of the distribution.

_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:

     'lmom.ub', 'lmomnor', 'cdfnor', 'quanor'

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

     lmr <- lmom.ub(rnorm(20))
     parnor(lmr)

     # A more extended example to explore the differences between an
     # L-moment derived estimate of the standard deviation and R's sd()
     true.std <- 15000 # select a large standard deviation
     std         <- vector(mode = "numeric") # vector of sd()
     std.by.lmom <- vector(mode = "numeric") # vector of L-scale values
     sam <- 7   # number of samples to simulate
     sim <- 100 # perform simulation sim times
     for(i in seq(1,sim)) {
       Q <- rnorm(sam,sd=15000) # draw random normal deviates
       std[i] <- sd(Q) # compute standard deviation
       lmr <- lmoms(Q) # compute the L-moments
       std.by.lmom[i] <- lmr$lambdas[2] # save the L-scale value
     }
     # convert L-scale values to equivalent standard deviations
     std.by.lmom      <- sqrt(pi)*std.by.lmom

     # compute the two biases and then output
     # see how the standard deviation estimated through L-scale
     # has a smaller bias than the usual (product moment) standard
     # deviation. The unbiasness of L-moments is demonstrated.
     std.bias         <- true.std - mean(std)
     std.by.lmom.bias <- true.std - mean(std.by.lmom)
     cat(c(std.bias,std.by.lmom.bias,"\n"))

