hypMode               package:fBasics               R Documentation

_H_y_p_e_r_b_o_l_i_c _M_o_d_e

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

     Computes the mode of the hyperbolic function.

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

     hypMode(alpha = 1, beta = 0, delta = 1, mu = 0, pm = c(1, 2, 3, 4))

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

alpha, beta, delta, mu: shape parameter 'alpha'; skewness parameter
          'beta', 'abs(beta)' is in the  range (0, alpha); scale
          parameter 'delta', 'delta' must be zero or  positive; 
          location parameter 'mu', 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'. 

      pm: an integer value between '1' and '4' for the  selection of
          the parameterization. The default takes the first
          parameterization.        

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

     returns the mode in the appropriate parameterization for the
     hyperbolic distribution. A numeric value.

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

     David Scott for code implemented from R's  contributed package
     'HyperbolicDist'.

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

     Atkinson, A.C. (1982);  _The simulation of generalized inverse
     Gaussian and hyperbolic  random variables_, SIAM J. Sci. Stat.
     Comput. 3, 502-515. 

     Barndorff-Nielsen O. (1977); _Exponentially decreasing
     distributions for the logarithm of  particle size_,  Proc. Roy.
     Soc. Lond., A353, 401-419. 

     Barndorff-Nielsen O., Blaesild, P. (1983);  _Hyperbolic
     distributions. In Encyclopedia of Statistical  Sciences_,  Eds.,
     Johnson N.L., Kotz S. and Read C.B.,  Vol. 3, pp. 700-707. New
     York: Wiley. 

     Raible S. (2000); _Levy Processes in Finance: Theory, Numerics and
     Empirical Facts_, PhD Thesis, University of Freiburg, Germany, 161
     pages.

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

        
     ## hypMode -
        hypMode()

