pp                  package:lmomco                  R Documentation

_P_l_o_t_t_i_n_g-_P_o_s_i_t_i_o_n _F_o_r_m_u_l_a

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

     The plotting positions of a data vector ('x') are returned in
     ascending order. The plotting-position formula is


                   pp_i = frac{i-a}{n+1-2a} mbox{,}


     where pp_i is the nonexceedance probability F of the ith ascending
     data value. The parameter a specifies the plotting-position type,
     and n is the sample size ('length(x)').

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

     pp(x,a=0)

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

       x: A vector of data values. The vector is used to get sample
          size through 'length()'.

       a: A value for the plotting-position formula. Default is 'A=0',
          which returns the Weibull plotting positions

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

     An R 'vector' is returned.

_N_o_t_e:

     Various plotting positions have been suggested in the literature.
     Stedinger and others (1992, p. 18.25) comment that "all plotting
     positions give crude estimates of the unknown [non]exceedance
     probabilities associated with the largest (and smallest) events."
     The various plotting positions are summarized in the follow table.

         \hline Name        a       Motivation
       \hline  Weibull      0       Unbiased exceedance probability for all distributions
           Median         0.3175    Median exceedance probabilities for all distributions
             APL        about 0.35  Often used with probability-weighted moments
            Blom          0.375     Nearly unbiased quantiles for normal distribution
           Cunnane         0.40     Approximately quantile unbiased
         Gringorten        0.44     Optimized for Gumbel distribution
            Hazen          0.50     A traditional choice
           \hline                   

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

     W.H. Asquith

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

     Stedinger, J.R., Vogel, R.M., and Foufoula-Georgiou, E., 1992,
     Frequency analysis of extreme events, in Handbook of Hydrology,
     chapter 18, editor-in-chief D. A. Maidment: McGraw-Hill, New York.

_S_e_e _A_l_s_o:

     'nonexceeds', 'pwm.pp'

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

     Q <- rnorm(20)
     PP <- pp(Q)
     plot(PP,sort(Q))

     Q <- rweibull(30,1.4,scale=400)
     WEI <- parwei(lmom.ub(Q))
     PP <- pp(Q)
     plot(PP,sort(Q))
     lines(PP,quawei(PP,WEI))

