dst                    package:sn                    R Documentation

_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:

     Density function, distribution function and random number
     generation for the skew-t (ST) distribution.

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

     dst(x, location=0, scale=1, shape=0, df=Inf)
     pst(x, location=0, scale=1, shape=0, df=Inf)
     qst(p, location=0, scale=1, shape=0, df=Inf, tol=1e-8)
     rst(n=1, location=0, scale=1, shape=0, df=Inf)

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

       x: vector of quantiles. Missing values (`NA's) are allowed. 

       p: vector of probabililities 

location: vector of location parameters. 

   scale: vector of (positive) scale parameters. 

   shape: vector of shape parameters. With `pst' and `qst',  it must be
          of length 1. 

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

       n: sample size. 

     tol: a scalar value which regulates the accuracy of the result of
          `qsn'. 

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

     Density (`dst'), probability (`pst'), quantiles (`qst')  and
     random sample (`rst') from the skew-t distribution with given 
     `location', `scale', `shape' and `df' parameters.

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

     The family of skew-t distributions is an extension of the
     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 Student's t distribution. When `df=Inf', it
     reduces to the  skew-normal distribution. A multivariate version
     of the distribution exists. 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:

     `dmst', `dsn', `st.mle'

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

     pdf <- dst(seq(-4,4,by=0.1), shape=3, df=5)
     rnd <- rst(100, 5, 2, -5, 8)
     q <- qst(c(0.25,0.5,0.75), shape=3, df=5)
     pst(q, shape=3, df=5)  # must give back c(0.25,0.5,0.75)

