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)
     psn(q, location=0, scale=1, shape=0)
     qsn(p, location=0, scale=1, shape=0, tol=1e-8)
     rsn(n=1, location=0, scale=1, shape=0)

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

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

       q: vector of quantiles. Missing values (`NA'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. 

       n: sample size. 

     tol: a scal value which regulates the accuracy of the result. 

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

     `psn' make use of function `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
     when `location=0' and `scale=1' is `2*dnorm(x)*pnorm(shape*x)'. A
     multivariate version of the distribution exists. See the
     references below for additional information.

_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.

     Azzalini, A. and Dalla Valle, A. (1996). The multivariate
     skew-normal distribution. Biometrika 83, 715-726.

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

     `T.Owen', `dmsn', `sn.mle'

_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)

