sged                 package:fGarch                 R Documentation

_S_k_e_w _G_E_D _D_i_s_t_r_i_b_u_t_i_o_n _a_n_d _P_a_r_a_m_e_t_e_r _E_s_t_i_m_a_t_i_o_n

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

     Functions to compute density, distribution function,  quantile
     function and to generate random variates  for the generalized
     error distribution. In addition maximum likelihood estimators are
     available  to fit the parameters of the distribution. 

     The functions are:

       '[dpqr]ged'   Symmetric GED Distribution,
       '[dpqr]sged'  Skew GED Distribution,
       'gedFit'      MLE parameter fit for a GED distribution,
       'sgedFit'     MLE parameter fit for a skew GED distribution,
       'sgedSlider'  Displays interactively skew GED distribution.

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

     dged(x, mean = 0, sd = 1, nu = 2)
     pged(q, mean = 0, sd = 1, nu = 2)
     qged(p, mean = 0, sd = 1, nu = 2)
     rged(n, mean = 0, sd = 1, nu = 2)

     dsged(x, mean = 0, sd = 1, nu = 2, xi = 1.5)
     psged(q, mean = 0, sd = 1, nu = 2, xi = 1.5)
     qsged(p, mean = 0, sd = 1, nu = 2, xi = 1.5)
     rsged(n, mean = 0, sd = 1, nu = 2, xi = 1.5)

     gedFit(x, ...)
     sgedFit(x, ...)

     sgedSlider(type = c("dist", "rand"))

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

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

       n: the number of observations. 

       p: a numeric vector of probabilities. 

    type: a character string denoting which interactive plot should be
          displayed. Either a distribution plot 'type="dist"', the
          default value, or a random variates plot, 'type="rand"'. 

    x, q: a numeric vector of quantiles. 

     ...: parameters parsed to the optimization function 'nlm'.  

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

     *Parameter Estimation:* 

      The function 'nlm' is used to minimize the "negative" maximum 
     log-likelihood function. 'nlm' carries out a minimization using  a
     Newton-type algorithm.

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

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

     '[s]gedFit' returns a list with the following components:  


     par: The best set of parameters found.  

objective: The value of objective corresponding to 'par'. 

convergence: An integer code. 0 indicates successful convergence. 

 message: A character string giving any additional information 
          returned by the optimizer, or NULL. For details, see  PORT
          documentation. 

iterations: Number of iterations performed. 

evaluations: Number of objective function and gradient function 
          evaluations. 

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

     Diethelm Wuertz for the Rmetrics R-port.

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

     Nelson D.B. (1991); _Conditional Heteroscedasticity in Asset
     Returns: A New Approach_, Econometrica, 59, 347-370.

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

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

     ## sged -
        par(mfrow = c(2, 2))
        set.seed(1953)
        r = rsged(n = 1000)
        plot(r, type = "l", main = "sged", col = "steelblue")
        
        # Plot empirical density and compare with true density:
        hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue")
        box()
        x = seq(min(r), max(r), length = 201)
        lines(x, dsged(x), lwd = 2)
        
        # Plot df and compare with true df:
        plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue",
          ylab = "Probability")
        lines(x, psged(x), lwd = 2)
        
        # Compute quantiles:
        round(qsged(psged(q = seq(-1, 5, by = 1))), digits = 6)
            
     ## sgedFit -
        sgedFit(r)
        
     ## sgedSlider -
        if (require(tcltk)) {
        sgedSlider("dist")
        sgedSlider("rand")
        }

