hypFit                package:fBasics                R Documentation

_F_i_t _o_f _a _H_y_p_e_r_b_o_l_i_c _D_i_s_t_r_i_b_u_t_i_o_n

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

     Estimates the parameters of a hyperbolic distribution.

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

         
     hypFit(x, alpha = 1, beta = 0, delta = 1, mu = 0, 
         scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE, 
         title = NULL, description = NULL, ...) 

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

alpha, beta, delta, mu: 'alpha' is a shape parameter by default 1,
          'beta' is a skewness parameter by default 0,  note
          'abs(beta)' is in the range (0, alpha), 'delta' is a scale
          parameter by default 1,  note, 'delta' must be zero or
          positive, and 'mu' is a location parameter, by default 0.
          These is the meaning of the parameters in the first 
          parameterization 'pm=1' which is the default 
          parameterization selection. In the second parameterization,
          'pm=2' 'alpha' and 'beta' take the meaning of the shape
          parameters (usually named) 'zeta' and 'rho'. In the third
          parameterization, 'pm=3' 'alpha' and 'beta' take the meaning
          of the shape parameters (usually named) 'xi' and 'chi'. In
          the fourth parameterization, 'pm=4' 'alpha' and 'beta' take
          the meaning of the shape parameters (usually named) 'a.bar'
          and 'b.bar'. 

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

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

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

    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? 

       x: a numeric vector.  

     ...: parameters to be parsed. 

_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 '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. 

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

         
     ## rhyp -
        # Simulate Random Variates:
        set.seed(1953)
        s = rhyp(n = 1000, alpha = 1.5, beta = 0.3, delta = 0.5, mu = -1.0) 

     ## hypFit -  
        # Fit Parameters:
        hypFit(s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE) 

