DistributionFits           package:fBasics           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 moment and maximum  likelihood
     estimators to fit the parameters of a  distribution.  

     The functions are:

       'nFit'       MLE parameter fit for a normal distribution,
       'tFit'       MLE parameter fit for a Student t-distribution,
       'stableFit'  MLE and Quantile Method stable parameter fit.

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

     nFit(x, doplot = TRUE, span = "auto", title = NULL, description = NULL, ...)
     tFit(x, df = 4, doplot = TRUE, span = "auto", trace = FALSE, title = NULL, 
         description = NULL, ...)
         
     stableFit(x, alpha = 1.75, beta = 0, gamma = 1, delta = 0, 
         type = c("q", "mle"), doplot = TRUE, trace = FALSE, title = NULL, 
         description = NULL) 
         
     ## S4 method for signature 'fDISTFIT':
     show(object)

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

alpha, beta, gamma, delta: [stable] - 
           The parameters are 'alpha', 'beta', 'gamma',  and 'delta':
           value of the index parameter 'alpha' with 'alpha = (0,2]';
          skewness parameter 'beta', in the range [-1, 1]; scale
          parameter 'gamma'; and shift parameter 'delta'. 

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

      df: the number of degrees of freedom for the Student
          distribution,  'df > 2', maybe non-integer. By default a
          value of 4 is assumed. 

  object: [show] - 
           an S4 class object as returned from the fitting functions. 

  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. 

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

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

    type: a character string which allows to select the method for
          parameter estimation: '"mle"', the maximum log likelihood
          approach, or '"qm"', McCulloch's quantile method. 

       x: a numeric vector.  

     ...: parameters to be parsed. 

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

     *Stable Parameter Estimation:*

     Estimation techniques based on the quantiles of an empirical
     sample  were first suggested by Fama and Roll [1971]. However
     their technique  was limited to symmetric distributions and
     suffered from a small  asymptotic bias. McCulloch [1986] developed
     a technique that uses  five quantiles from a sample to estimate
     'alpha' and 'beta' without asymptotic bias. Unfortunately, the
     estimators provided by McCulloch have restriction 'alpha>0.6'.

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

     The functions 'tFit', 'hypFit' and 'nigFit' return  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. 


     Remark: The parameter estimation for the stable distribution via
     the  maximum Log-Likelihood approach may take a quite long time.

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

         
     ## nFit -
        # Simulate random normal variates N(0.5, 2.0):
        set.seed(1953)
        s = rnorm(n = 1000, 0.5, 2) 

     ## nigFit -  
        # Fit Parameters:
        nFit(s, doplot = TRUE) 

