cardioid                package:VGAM                R Documentation

_C_a_r_d_i_o_i_d _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 the cardioid distribution by
     maximum likelihood estimation.

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

     cardioid(lmu="elogit", lrho="elogit",
              emu=if(lmu=="elogit") list(min=0, max=2*pi) else list(),
              erho=if(lmu=="elogit") list(min=-0.5, max=0.5) else list(),
              imu=NULL, irho=0.3, nsimEIM=100, zero=NULL)

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

lmu, lrho: Parameter link functions applied to the mu and rho
          parameters, respectively. See 'Links' for more choices.

emu, erho: List. Extra argument for each of the link functions. See
          'earg' in 'Links' for general information.

imu, irho: Initial values. A 'NULL' means an initial value is chosen
          internally. See 'CommonVGAMffArguments' for more information.

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

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

     The two-parameter cardioid distribution  has a density that can be
     written as

             f(y;mu,rho) = (1 + 2*rho*cos(y-mu)) / (2*pi)

     where 0 < y < 2*pi, 0 < mu < 2*pi, and  -0.5 < rho < 0.5 is the
     concentration parameter. The default link functions enforce the
     range constraints of the parameters.

     For positive rho the distribution is unimodal and symmetric about
     mu. The mean of Y (which make up the fitted values) is pi +
     (rho/pi) ((2*pi-mu)*sin(2*pi-mu) + cos(2*pi-mu) - mu*sin(mu) -
     cos(mu)).

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

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

_W_a_r_n_i_n_g:

     Numerically, this distribution can be difficult to fit because of
     a log-likelihood having multiple maxima. The user is therefore
     encouraged to try different starting values, i.e., make use of
     'imu' and 'irho'.

_N_o_t_e:

     Fisher scoring using simulation is used.

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

     T. W. Yee

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

     Jammalamadaka, S. R. and SenGupta, A. (2001) _Topics in Circular
     Statistics_, Singapore: World Scientific.

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

     'rcard', 'elogit', 'vonmises'.

     'CircStats' and 'circular' currently have a lot more R functions
     for circular data than the 'VGAM' package.

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

     y = rcard(n=1000, mu=4, rho=0.45)
     fit = vglm(y ~ 1, cardioid, trace=TRUE) 
     coef(fit, matrix=TRUE)
     Coef(fit)
     c(mean(y), fitted(fit)[1,])
     summary(fit)

