sghFit                package:fBasics                R Documentation

_S_t_a_n_d_a_r_d_i_z_e_d _G_H _D_i_s_t_r_i_b_u_t_i_o_n _F_i_t

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

     Estimates the distrinbutional parameters for a  standardized
     generalized hyperbolic distribution.

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

     sghFit(x, zeta = 1, rho = 0, lambda = 1, include.lambda = TRUE,
         scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE, 
         title = NULL, description = NULL, ...) 

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

       x: a numeric vector.  

zeta, rho, lambda: shape parameter 'zeta' is positive, skewness
          parameter 'rho' is in the range (-1, 1). and index parameter
          'lambda', by default 1. 

include.lambda: a logical flag, by default 'TRUE'. Should the index
          parameter 'lambda' included in the parameter estimate? 

   scale: a logical flag, by default 'TRUE'. Should the time series be
          scaled by its standard deviation to achieve a more stable
          optimization? 

  doplot: a logical flag. Should a plot be displayed? 

    span: x-coordinates for the plot, by default 100 values 
          automatically selected and ranging between the 0.001,  and
          0.999 quantiles. Alternatively, you can specify the range by
          an expression like 'span=seq(min, max, times = n)', where,
          'min' and 'max' are the  left and right endpoints of the
          range, and 'n' gives  the number of the intermediate points. 

   trace: a logical flag. Should the parameter estimation process be
          traced? 

   title: a character string which allows for a project title. 

description: a character string which allows for a brief description. 

     ...: parameters to be parsed. 

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

     returns a list with the following components:

estimate: the point at which the maximum value of the log liklihood 
          function is obtained. 

 minimum: the value of the estimated maximum, i.e. the value of the log
          liklihood function. 

    code: an integer indicating why the optimization process
          terminated.
           1: relative gradient is close to zero, current iterate is
          probably  solution; 
           2: successive iterates within tolerance, current iterate is
          probably  solution; 
           3: last global step failed to locate a point lower than
          'estimate'.  Either 'estimate' is an approximate local
          minimum of the  function or 'steptol' is too small; 
           4: iteration limit exceeded; 
           5: maximum step size 'stepmax' exceeded five consecutive
          times.  Either the function is unbounded below, becomes
          asymptotic to a  finite value from above in some direction or
          'stepmax'  is too small. 

gradient: the gradient at the estimated maximum. 

   steps: number of function calls. 

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

         
     ## sghFit -
        # Simulate Random Variates:
        set.seed(1953)
        s = rsgh(n = 2000, zeta = 0.7, rho = 0.5, lambda = 0) 

     ## sghFit -  
        # Fit Parameters:
        sghFit(s, zeta = 1, rho = 0, lambda = 1, include.lambda = TRUE, 
          doplot = TRUE) 

