serum             package:hyperdirichlet             R Documentation

_S_e_r_u_m _d_a_t_a _f_r_o_m _M_o_s_i_m_a_n_n _1_9_6_2

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

     Data from Mosimann 1962 detailing serum proteins in white Pekin
     ducklings.

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

     data(serum)

_F_o_r_m_a_t:

     A matrix with three columns and 23 rows.

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

     The rows each sum to 1; the values are the relative frequencies of
     serum proteins in white Pekin ducklings as determined by
     electrophores.

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

     J. E. Mosimann 1962.  On the compound multinomial distribution,
     the multivariate beta-distribution, and correlations among
     proportions.  _Biometrika_, volume 49, numbers 1 and 2, pp65-82.

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

     data(serum)
     dhyperdirichlet(serum , HD=dirichlet(4:6),log=TRUE)

     f <- function(x){
       if(any(x<0)){
         return(Inf)
       } else {
         return(-sum(dhyperdirichlet(serum , HD=dirichlet(x),include.NC=TRUE,log=TRUE)))
       }
     }

     fish <- optim(c(3.21,20.38,21.68),f)
     triplot(HD=dirichlet(fish$par),l=60,main="increase 'l' for better plot quality")
     points(serum[,1]+serum[,2]/2,serum[,2]*sqrt(3)/2,pch=16)

