dsn                    package:sn                    R Documentation

_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:

     Density function, distribution function, quantiles and random
     number generation for the skew-normal (SN) distribution.

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

     dsn(x, location=0, scale=1, shape=0, log=FALSE)
     dsn(x, dp=, log=FALSE)
     psn(x, location=0, scale=1, shape=0, engine, ...)
     psn(x, dp=, engine, ...)
     qsn(p, location=0, scale=1, shape=0, tol=1e-8, ...)
     qsn(x, dp=, ...)
     rsn(n=1, location=0, scale=1, shape=0)
     rsn(x, dp=)

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

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

       p: vector of probabilities. Missing values ('NA's) are allowed. 

location: vector of location parameters. 

   scale: vector of (positive) scale parameters. 

   shape: vector of shape parameters. With 'psn' and 'qsn', it must be
          of length 1. 

      dp: a vector of length 3, whose elements represent location,
          scale (positive)  and shape, respectively. If 'dp' is
          specified, the individual parameters cannot be set. 

       n: sample size. 

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

     log: logical flag used in 'dsn' (default 'FALSE'). When 'TRUE',
          the logarithm of the density values is returned. 

  engine: character string to select the computing engine, which is
          either '"T.Owen"' or '"biv.nt.prob"' (the latter from package
           'mnormt'). If the parameter is missing, a default selection
          rule is applied. 

     ...: additional parameters passed to 'T.Owen' 

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

     density ('dsn'), probability ('psn'), quantile ('qsn') or  random
     sample ('rsn') from the skew-normal distribution with given
     'location', 'scale' and 'shape' parameters.

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

     The family of skew-normal distributions is an extension of the
     normal family, via the introdution of a 'shape' parameter which
     regulates skewness; when 'shape=0', the skew-normal distribution
     reduces to the normal one.  The density of the SN distribution in
     the "standard" case having 'location=0' and 'scale=1'  is
     '2*dnorm(x)*pnorm(shape*x)'. A multivariate version of the
     distribution exists. See the reference below for additional
     information.

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

     'psn' and 'qsn' make use either of function 'T.Owen' or
     'biv.nt.prob'

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

     Azzalini, A. (1985). A class of distributions which includes the
     normal ones. _Scand. J. Statist._ *12*, 171-178.

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

     'dmsn', 'dst',  'T.Owen', 'biv.nt.prob'

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

     pdf <- dsn(seq(-3,3,by=0.1), shape=3)
     cdf <- psn(seq(-3,3,by=0.1), shape=3)
     qu <- qsn(seq(0.1,0.9,by=0.1), shape=-2)
     rn <- rsn(100, 5, 2, 5)

