ght                 package:fBasics                 R Documentation

_G_e_n_e_r_a_l_i_z_e_d _H_y_p_e_r_b_o_l_i_c _S_t_u_d_e_n_t-_t

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

     Density, distribution function, quantile function  and random
     generation for the hyperbolic distribution.

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

     dght(x, beta = 0.1, delta = 1, mu = 0, nu = 10)
     pght(q, beta = 0.1, delta = 1, mu = 0, nu = 10)
     qght(p, beta = 0.1, delta = 1, mu = 0, nu = 10)
     rght(n, beta = 0.1, delta = 1, mu = 0, nu = 10)

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

    x, q: a numeric vector of quantiles. 

       p: a numeric vector of probabilities. 

       n: number of observations. 

beta, delta, mu: 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 are the parameters in the first parameterization. 

      nu: a numeric value, the number of degrees of freedom. 

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

     All values for the '*ght' functions are numeric vectors:  'd*'
     returns the density, 'p*' returns the distribution function, 'q*'
     returns the quantile function, and 'r*' generates random deviates.

     All values have attributes named '"param"' listing the values of
     the distributional parameters.

_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:

        
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