quacau                package:lmomco                R Documentation

_Q_u_a_n_t_i_l_e _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 quantiles of the Cauchy distribution
     given parameters (xi and alpha) of the distribution provided by
     'vec2par'. The quantile function of the distribution is


            x(F) = xi + alpha times tan(pi(F-0.5)) mbox{,}


     where x(F) is the quantile for nonexceedance probability F, xi is
     a location parameter and alpha is a scale parameter. R supports
     the quantile function of the Cauchy distribution through
     'qcauchy'. This function does not use 'qcauchy' because 'qcauchy'
     does not return 'Inf' for F = 1 although it returns '-Inf' for F =
     0.

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

     quacau(f, para)

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

       f: Nonexceedance probability (0 <= F <= 1).

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

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

     Quantile value for for nonexceedance probability F.

_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.

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

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

     'cdfcau', 'parcau', 'vec2par'

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

       para <- c(12,12)
       quacau(.5,vec2par(para,type='cau'))

