cdfcau                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 _C_a_u_c_h_y _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 Cauchy distribution given parameters (xi and
     alpha) of the distribution provided by 'parcau' or 'vec2par'.  The
     cumulative distribution function of the distribution is


       F(x) = frac{arctan(frac{x - xi}{alpha})}{pi}+0.5 mbox{,}


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

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

     cdfcau(x, para)

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

       x: A real value.

    para: The parameters from 'parcau' or 'vec2par'.

_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:

     Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments:
     Computational Statistics and Data Analysis, vol. 43, pp. 299-314.

     Gilchrist, W.G., 2000, Statistical modeling with quantile
     functions:  Chapman and Hall/CRC, Boca Raton, FL.

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

     'quacau', 'parcau', 'vec2par'

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

       para <- c(12,12)
       cdfcau(50,vec2par(para,type='cau'))

