SkewNormalDistribution        package:fSeries        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:

     A collection and description of functions to compute  density,
     distribution function, quantile function and  to generate random
     variates for the skew normal  distribution.  

     The functions are:

       '[dpqr]norm'   Normal distribution from R's base package,
       '[dpqr]snorm'  Skew Normal distribution.

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

     dsnorm(x, mean = 0, sd = 1, xi = 1.5)
     psnorm(q, mean = 0, sd = 1, xi = 1.5)
     qsnorm(p, mean = 0, sd = 1, xi = 1.5)
     rsnorm(n, mean = 0, sd = 1, xi = 1.5)

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

mean, sd, xi: location parameter 'mean', scale parameter 'sd', skewness
          parameter 'xi'. 

       n: number of observations. 

       p: a numeric vector of probabilities. 

    x, q: a numeric vector of quantiles. 

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

     *Symmetric Normal Distibution:* 

      The functions for the normal distribution are part of R's base
     package. 

     *Skew Normal Distribution:* 

      The skew normal distribution functions are defined as described
     by Fernandez and Steel (2000).

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

     All values are numeric vectors: 'd*' returns the density, 'p*'
     returns the distribution function, 'q*' returns the quantile
     function, and 'r*' generates random deviates.

_A_u_t_h_o_r(_s):

     Diethelm Wuertz for the Rmetrics R-port.

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

     Fernandez C., Steel M.F.J. (2000);  _On Bayesian Modelling of Fat
     Tails and Skewness_, Preprint, 31 pages.

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

     'sstdDistribution', 'sgedDistribution'.

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

     ## snorm -
        xmpSeries("\nStart: Skew Normal Distribuion:  > ")
        par(mfrow = c(2, 2), cex = 0.75)
        set.seed(1953)
        r = rsnorm(n = 1000, mean = 1, sd = 0.5, xi = 1.5)
        plot(r, type = "l", main = "snorm: xi = 1.5")
        # Plot empirical density and compare with true density:
        hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue4")
        x = seq(-4, 6, 0.1)
        lines(x, dsnorm(x = x, mean = 1, sd = 0.5, xi = 1.5))
        # Plot df and compare with true df:
        plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue4")
        lines(x, psnorm(x, mean = 1, sd = 0.5, xi = 1.5))
        # Compute quantiles:
        qsnorm(psnorm(q = -4:6, mean = 1, sd = 0.5, xi = 1.5), 
          mean = 1, sd = 0.5, xi = 1.5) 

