dmsn                   package:sn                   R Documentation

_M_u_l_t_i_v_a_r_i_a_t_e _s_k_e_w-_n_o_r_m_a_l _d_i_s_t_r_i_b_u_t_i_o_n

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

     Probability density function and random number generation for the
     multivariate skew-normal (MSN) distribution.

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

     dmsn(x, xi=rep(0,k), Omega, alpha)
     rmsn(n=1, xi=rep(0,k), Omega, alpha)

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

       x: either a vector of length `k' or a matrix with `k' columns,
          where `k' is `length(alpha)', giving the coordinates of the
          point(s) where the density must be avaluated. 

   Omega: a covariance matrix of dimension `(k,k)'. 

   alpha: a numeric vector which regulates the shape of the density. 

      xi: a numeric vector of lenght `k', or a matrix with `k' columns,
          representing the location parameter of the distribution. If
          `xi' is a matrix, its dimensions must agree with those of
          `x'. 

       n: a numeric value which represents the number of random vectors
          to be drawn. 

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

     A vector of density values (`dmsn'), or a matrix of random  points
     (`rmsn').

_B_a_c_k_g_r_o_u_n_d:

     The multivariate skew-normal distribution is discussed by Azzalini
     and Dalla Valle (1996); the `(Omega,alpha)' parametrization
     adopted here is the one of Azzalini and Capitanio (1999).

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

     Azzalini, A. and Dalla Valle, A. (1996). The multivariate
     skew-normal distribution. Biometrika 83, 715-726.

     Azzalini, A. and Capitanio, A. (1999). Statistical applications of
     the multivariate skew-normal distribution. J.Roy.Statist.Soc. B
     61, 579-602.

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

     `dsn', `msn.fit', `msn.quantities'

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

     x <- seq(-3,3,length=30)
     pdf <- dmsn(cbind(x,0), c(0,0), diag(2), c(2,3))
     #
     rnd <- rmsn(50,  c(0,0), diag(2), c(2,3))

