A1inv               package:CircStats               R Documentation

_I_n_v_e_r_s_e _o_f _A_1

_D_e_s_c_r_i_p_t_i_o_n:

     Inverse function of the ratio of the first and zeroth order Bessel
     functions of the first kind.  This function is used to compute the
     maximum likelihood estimate of the concentration parameter of a
     von Mises distribution.

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

     A1inv(x)

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

       x: numeric value in the interval between 0 and 1.

_D_e_t_a_i_l_s:

     A1inv(0) = 0 and A1inv(1) = inf.  This function is useful in
     estimating the concentration parameter of data from a von Mises
     distribution.

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

     Returns the value k, such that A1inv(x) = k, i.e. A1(k) = x.

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

     `est.kappa', `A1', `besselI'.

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

     #Generate data from a von Mises distribution
     data <- rvm(50, pi, 4)
     #Estimate the concentration parameter
     s <- sum(sin(data))
     c <- sum(cos(data))
     mean.dir <- atan(s, c)
     kappa <- A1inv(mean(cos(data - mean.dir)))

