riceff                 package:VGAM                 R Documentation

_R_i_c_e _D_i_s_t_r_i_b_u_t_i_o_n _F_a_m_i_l_y _F_u_n_c_t_i_o_n

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

     Estimates the two parameters of a Rice distribution by maximum
     likelihood estimation.

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

     riceff(lvee="loge", lsigma="loge",
            evee=list(), esigma=list(),
            ivee=NULL, isigma=NULL,
            nsimEIM=100, zero=NULL)

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

lvee, evee: Link function and extra argument for the v parameter. See
          'Links' for more choices and for general information.

lsigma, esigma: Link function and extra argument for the sigma
          parameter. See 'Links' for more choices and for general
          information.

ivee, isigma: Optional initial values for the parameters. See
          'CommonVGAMffArguments' for more information. If convergence
          failure occurs (this 'VGAM' family function seems to require
          good initial values) try using these arguments.

nsimEIM, zero: See 'CommonVGAMffArguments' for more information.

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

     The Rician distribution has density function

 f(y;v,sigma) =  (y/sigma^2) * exp(-(y^2+v^2) / (2*sigma^2)) * I_0(y*v/sigma^2)

     where y>0, v > 0, sigma > 0 and I_0 is the modified Bessel
     function of the first kind with order zero. When v=0 the Rice
     distribution reduces to a Rayleigh distribution. The mean is
     sigma*sqrt(pi/2)*exp(z/2)*((1-z)*I_0(-z/2)-z*I_1(-z/2)) (returned
     as the fitted values) where z=-v^2/(2*sigma^2). Simulated Fisher
     scoring is implemented.

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

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm' and 'vgam'.

_N_o_t_e:

     Convergence problems may occur for data where v=0; if so, use
     'rayleigh' or possibly use an 'identity' link.

     When v is large (greater than 3, say) then the mean is
     approximately v and the standard deviation is approximately sigma.

_A_u_t_h_o_r(_s):

     T. W. Yee

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

     Rice, S. O. (1945) Mathematical Analysis of Random Noise. _Bell
     System Technical Journal_, *24*, 46-156.

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

     'drice', 'rayleigh', 'besselI'.

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

     vee = exp(2); sigma = exp(1);
     y = rrice(n <- 1000, vee, sigma)
     fit = vglm(y ~ 1, riceff, trace=TRUE, crit="c")
     c(mean(y), fitted(fit)[1])
     coef(fit, matrix=TRUE)
     Coef(fit)
     summary(fit)

