GarchDistributionFits        package:fSeries        R Documentation

_P_a_r_a_m_e_t_e_r _F_i_t _o_f _a _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 maximum likelihood  estimators to
     fit the parameters of a distribution  and to compute basic
     statistical properties. Included  are estimators for the symmetric
     and skew normal,  the Student-t, and the generalized error
     distributions.  

     The functions are:

       'normFit'   MLE parameter fit for a Normal distribution,
       'snormFit'  MLE parameter fit for a skew Normal distribution,
       'stdFit'    MLE parameter fit for a Sudent-t distribution,
       'stdFit'    MLE parameter fit for a skew Sudent-t distribution,
       'gedFit'    MLE parameter fit for a generalized error distribution,
       'nigFit'    MLE parameter fit for a skew generalized error distribution.

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

     normFit(x, ...)
     snormFit(x, ...)
     stdFit(x, ...)
     sstdFit(x, ...)
     gedFit(x, ...)
     sgedFit(x, ...)

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

       x: a numeric vector. 

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

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

     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:

     The functions '*Fit' return a list with the following components:

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

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

 message: an integer indicating why the optimization process
          terminated. 

    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. 

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

     Diethelm Wuertz for the Rmetrics R-port.

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

     'dsnorm', 'dsstd',  'dsged',  'nlm'.

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

     ## snormFit -
        xmpSeries("\nStart: MLE Fit to skew Normal Density > ")
        options(warn = -1) # suppress negative logs from nlm
        normFit(rnorm(1000))
        snormFit(rnorm(1000))
        
     ## sstdFit -
        xmpSeries("\nNext: MLE Fit to skew Student-t Density > ")
        sstdFit(rsstd(1000, mean = 1, sd = 1.5, nu = 7, xi = 2/3))
        
     ## sgedFit -
        xmpSeries("\nNext: MLE Fit to skew Generalized Error Density > ")
        sgedFit(rsged(1000, mean = -1, sd = 0.5, nu = 3, xi = 3/2),
              print.level = 2)

