dmst                   package:sn                   R Documentation

_M_u_l_t_i_v_a_r_i_a_t_e _s_k_e_w-_t _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-t (MST) distribution.

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

     dmst(x, xi=rep(0,d), Omega, alpha, df=Inf)
     pmst(x, xi=rep(0,d), Omega, alpha, df=Inf, ...)
     rmst(n=1, xi=rep(0,d), Omega, alpha, df=Inf)

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

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

      xi: a numeric vector of lenght `d', or a matrix with `d' columns,
          representing the location parameter of the distribution. If
          `xi' is a matrix, 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. 

      df: degrees of freedom (scalar); default is `df=Inf' which
          corresponds  to the multivariate skew-normal distribution. 

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

     ...: additional parameters passed to `pmvt' 

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

     The positive-definiteness of `Omega' is not tested for efficiency
     reasons. Function `pmst' requires `pmvt' from `library(mvtnorm)';
     the accuracy of its computation can be controlled via use of `...'

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

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

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

     The family of multivariate skew-t distributions is an extension of
     the  multivariate Student's t family, via the introduction of a
     `shape'  parameter which regulates skewness; when `shape=0', the
     skew-t  distribution reduces to the usual t distribution.  When
     `df=Inf' the distribution reduces to the multivariate skew-normal 
     one; see `dmsn'. See the reference below for additional
     information.

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

     Azzalini, A. and Capitanio, A. (2003). Distributions generated by
     perturbation of symmetry  with emphasis on a multivariate skew t
     distribution. J.Roy. Statist. Soc. B 65, 367-389.

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

     `dst', `mst.fit', `dmsn', `pmvt'

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

     x <- seq(-4,4,length=15)
     xi <- c(0.5, -1)
     Omega <- diag(2)
     Omega[2,1] <- Omega[1,2] <- 0.5
     alpha <- c(2,2)
     pdf <- dmst(cbind(x,2*x-1), xi, Omega, alpha, df=5)
     rnd <- rmst(10,  xi, Omega, alpha, 6)
     library(mvtnorm)                # only once in the session
     cdf <- pmst(c(2,1), xi, Omega, alpha, df=5)

