dwrpnorm              package:CircStats              R Documentation

_W_r_a_p_p_e_d _N_o_r_m_a_l _D_e_n_s_i_t_y _F_u_n_c_t_i_o_n

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

     Estimate of the wrapped normal density function.

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

     dwrpnorm(theta, mu, rho, sd=1, acc=1e-5, tol=acc)

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

   theta: value at which to evaluate the density function, measured in
          radians.

      mu: mean direction of distribution, measured in radians.

     rho: mean resultant length of distribution.

      sd: different way of select 'rho', see details below.

     acc: parameter defining the accuracy of the estimation of the
          density.  Terms are added to the infinite summation that
          defines the density function until successive estimates are
          within 'acc' of each other.

     tol: the same as 'acc'.

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

     The form of the wrapped normal density function is an infinite
     series with index going from negative infinity to positive
     infinity.  This function begins with the zeroth term and adds
     terms to the series, corresponding to both the positive and
     negative index, until the summation changes by less than the
     parameter value of 'acc'. You can set 'rho' by using 'sd' with the
     following equivalence:

                        rho = exp{- sigma^2/2}

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

     Returns an estimate of the wrapped normal density function.

_R_e_f_e_r_e_n_c_e_s:

     Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular
     Statistics, Section 2.2.6, World Scientific Press, Singapore.

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

     rwrpnorm

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

     # Values for which to evaluate density
     theta <- c(1:500)*2*pi/500
     #Compute wrapped normal density function
     density <- c(1:500)
     for(i in 1:500) density[i] <- dwrpnorm(theta[i], pi, .75)
     plot(theta, density)
     #Approximate area under density curve
     sum(density*2*pi/500)

