cdfgno                package:lmomco                R Documentation

_C_u_m_u_l_a_t_i_v_e _D_i_s_t_r_i_b_u_t_i_o_n _F_u_n_c_t_i_o_n _o_f _t_h_e _G_e_n_e_r_a_l_i_z_e_d _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 computes the cumulative probability or nonexceedance
     probability of the Generalized Normal distribution given
     parameters (xi, alpha, and kappa) of the distribution computed by
     'pargno'. The cumulative distribution function of the distribution
     is


                        F(x) = Phi(y) mbox{,}

     where Phi is the cumulative ditribution function of the standard
     normal distribution and y is


 y = -kappa^{-1} log(1 - frac{kappa(x-xi)}{alpha}) mbox { for } kappa ne 0 mbox{, and}



            y = (x-xi)/alpha mbox{ for } kappa = 0 mbox{,}

     where F(x) is the nonexceedance probability for quantile x, xi is
     a location parameter, alpha is a scale parameter, and kappa is a
     shape parameter.

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

     cdfgno(x, para)

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

       x: A real value.

    para: The parameters from 'pargno' or similar.

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

     Nonexceedance probability (F) for x.

_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:

     'quagno', 'pargno'

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

       lmr <- lmom.ub(c(123,34,4,654,37,78))
       cdfgno(50,pargno(lmr))

