

Cauchy {base}                                R Documentation

_T_h_e _C_a_u_c_h_y _D_i_s_t_r_i_b_u_t_i_o_n

_U_s_a_g_e_:

     dcauchy(x, location = 0, scale = 1)
     pcauchy(q, location = 0, scale = 1)
     qcauchy(p, location = 0, scale = 1)
     rcauchy(n, location = 0, scale = 1)

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

     x,q: vector of quantiles.

       p: vector of probabilities.

       n: number of observations to generate.

location,scale: location and scale parameters.

_V_a_l_u_e_:

     These functions provide information about the Cauchy
     distribution with location parameter `location' and
     scale parameter `scale'.

     `dcauchy', `pcauchy', and `qcauchy' are respectively
     the density, distribution function and quantile func-
     tion of the Cauchy distribution.  `rcauchy' generates
     random deviates from the Cauchy.

     If `location' or `scale' are not specified, they assume
     the default values of `0' and `1' respectively.

     The Cauchy distribution with location l and scale s has
     density

               f(x) = 1 / (pi s (1 + ((x-l)/s)^2))

     for all x.

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

     `dt' for the t distribution which generalizes
     `dcauchy(*, l = 0, s = 1)'.

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

     all.equal(dcauchy(-1:4), 1 / (pi*(1 + (-1:4)^2)))

