rmvt.mixt, dmvt.mixt           package:ks           R Documentation

_M_u_l_t_i_v_a_r_i_a_t_e _t _m_i_x_t_u_r_e _d_i_s_t_r_i_b_u_t_i_o_n

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

     Random generation and density values from multivariate t mixture 
     distribution.

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

     rmvt.mixt(n=100, mus=c(0,0), Sigmas=diag(2), dfs=7, props=1)
     dmvt.mixt(x, mus, Sigmas, dfs, props)

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

       n: number of random variates

       x: matrix of quantiles

     mus: (stacked) matrix of location vectors

  Sigmas: (stacked) matrix of dispersion matrices

     dfs: vector of degrees of freedom

   props: vector of mixing proportions

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

     'rmvt.mixt' is based on the 'rmvt' function from the 'mvtnorm'
     library.

     The formula for a d-variate t density with location vector mu,
     dispersion matrix Sigma and df degrees of freedom is

      k * (1 + 1/df * (x-mu)^T * Sigma^(-1) (x-mu))^(-(d+df)/2)

     where

 k = gamma((df+d)/2) / ((df*pi)^(d/2) * gamma(df/2)* det(Sigma)^(1/2).

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

     Multivariate t mixture random vectors and density values.

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

     'rmvnorm.mixt', 'dmvnorm.mixt'

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

     mus <- rbind(c(-3/2,0), c(3/2,0))
     Sigmas <- rbind(diag(c(1/16, 1)), rbind(c(1/16, 1/18), c(1/18, 1/16)))
     props <- c(2/3, 1/3)
     dfs <- c(7,3)
     x <- rmvt.mixt(1000, mus, Sigmas, dfs, props)
     dens <- dmvt.mixt(x, mus, Sigmas, dfs, props)

