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

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

     dmsn(x, xi=rep(0,length(alpha)), Omega, alpha, log=FALSE)
     dmsn(x, dp=, log=FALSE)
     pmsn(x, xi=rep(0,length(alpha)), Omega, alpha, ...)
     pmsn(x, dp=)
     rmsn(n=1, xi=rep(0,length(alpha)), Omega, alpha)
     rmsn(n=1, dp=)

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

       x: for 'dmsn', this is either a vector of length 'd',  where
          'd=length(alpha)', or a matrix with 'd' columns,  giving the
          coordinates of the point(s) where the density must  be
          evaluated; for 'pmsn', only a vector of length 'd' is
          allowed. 

      xi: a numeric vector of length 'd' representing the location
          parameter of the distribution. In a call to 'dmsn', 'xi' can
          be a matrix;  in this case, its dimensions must agree with
          those of 'x'. 

   Omega: a positive-definite covariance matrix of dimension '(d,d)'. 

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

      dp: a list with three elements named 'xi', 'Omega' and 'alpha'
          containing quantities as described above. If 'dp' is
          specified, this overrides the individual parameter
          specification.  

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

     log: logical; if TRUE, densities  are given as log-densities. 

     ...: additional parameters passed to 'pmnorm' 

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

     The positive-definiteness of 'Omega' is not tested for efficiency
     reasons. Function 'pmsn' requires 'pmnorm' from package 'mnormt';
     the accuracy of its computation can be controlled via use of '...'

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

     A vector of density values ('dmsn'), or a single probability 
     ('pmsn') 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',  'dmst', 'dmnorm'

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

     x <- seq(-3,3,length=15)
     xi <- c(0.5, -1)
     Omega <- diag(2)
     Omega[2,1] <- Omega[1,2] <- 0.5
     alpha <- c(2,-6)
     pdf <- dmsn(cbind(x,2*x-1), xi, Omega, alpha)
     rnd <- rmsn(10,  xi, Omega, alpha)
     p1 <- pmsn(c(2,1), xi, Omega, alpha)
     p2 <- pmsn(c(2,1), xi, Omega, alpha, abseps=1e-12, maxpts=10000)

