cdfpe3                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 _P_e_a_r_s_o_n _T_y_p_e _I_I_I _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 Pearson Type III distribution given parameters
     (xi, alpha, and gamma) of the distribution computed by 'parpe3'.
     The cumulative distribution function of the distribution is


   F(x) = frac{G(alpha,frac{x - xi}{gamma})}{Gamma(alpha)} mbox{,}


     where F(x) is the nonexceedance probability for quantile x, G is
     the incomplete gamma function, Gamma is the gamma function, xi is
     a location parameter, alpha is a scale parameter, and gamma is a
     shape parameter.

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

     cdfpe3(x, para)

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

       x: A real value.

    para: The parameters from 'parpe3' 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:

     'quape3', 'parpe3'

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

       lmr <- lmom.ub(c(123,34,4,654,37,78))
       cdfpe3(50,parpe3(lmr))

