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,length(alpha)), Omega, alpha, df=Inf, log=FALSE)
     dmst(x, dp=, log=FALSE)
     pmst(x, xi=rep(0,length(alpha)), Omega, alpha, df=Inf, ...)
     pmst(x, dp=, ...)
     rmst(n=1, xi=rep(0,length(alpha)), Omega, alpha, df=Inf)
     rmst(n=1, dp=)

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

       x: for 'dmst', 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 
          avaluated; for 'pmst', 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. 

      dp: a list with three elements named 'xi', 'Omega', 'alpha' and
          'df', 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 'pmt' 

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

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

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

     A vector of density values ('dmst') or a single probability 
     ('pmst') 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',  'dmsn', 'dmt'

_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)
     p1 <- pmst(c(2,1), xi, Omega, alpha, df=5)
     p2 <- pmst(c(2,1), xi, Omega, alpha, df=5, abseps=1e-12, maxpts=10000)

