snig                 package:fBasics                 R Documentation

_S_t_a_n_d_a_r_d_i_z_e_d _N_o_r_m_a_l _I_n_v_e_r_s_e _G_a_u_s_s_i_a_n _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Density, distribution function, quantile function  and random
     generation for the standardized normal  inverse Gaussian
     distribution.

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

     dsnig(x, zeta = 1, rho = 0, log = FALSE)
     psnig(q, zeta = 1, rho = 0)
     qsnig(p, zeta = 1, rho = 0)
     rsnig(n, zeta = 1, rho = 0)

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

zeta, rho: shape parameter 'zeta' is positive, skewness parameter 'rho'
          is in the range (-1, 1). 

     log: a logical flag by default 'FALSE'.  If TRUE, log values are
          returned. 

       n: number of observations. 

       p: a numeric vector of probabilities. 

    x, q: a numeric vector of quantiles. 

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

     The random deviates are calculated with the method described by 
     Raible (2000).

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

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

     All values have attributes named '"param"' listing the values of
     the distributional parameters.

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

     Diethelm Wuertz.

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

        
     ## snig -
        set.seed(1953)
        r = rsnig(5000, zeta = 1, rho = 0.5)
        plot(r, type = "l", col = "steelblue",
          main = "snig: zeta=1 rho=0.5")
      
     ## snig - 
        # Plot empirical density and compare with true density:
        hist(r, n = 50, probability = TRUE, border = "white", col = "steelblue")
        x = seq(-5, 5, length = 501)
        lines(x, dsnig(x, zeta = 1, rho = 0.5))
      
     ## snig -  
        # Plot df and compare with true df:
        plot(sort(r), (1:5000/5000), main = "Probability", col = "steelblue")
        lines(x, psnig(x, zeta = 1, rho = 0.5))
        
     ## snig -
        # Compute Quantiles:
        qsnig(psnig(seq(-5, 5, 1), zeta = 1, rho = 0.5), zeta = 1, rho = 0.5) 

