

Generalized Inverse Gaussian(rmutil)         R Documentation

_T_h_e _G_e_n_e_r_a_l_i_z_e_d _I_n_v_e_r_s_e _G_a_u_s_s_i_a_n _D_i_s_t_r_i_b_u_t_i_o_n

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

     These functions provide information about the general-
     ized inverse Gaussian distribution with mean equal to
     `m', dispersion equal to `s', and family parameter
     equal to `f'.  `dginvgauss' gives the density, `pgin-
     vgauss' gives the distribution function.

     The generalized inverse Gaussian distribution has den-
     sity

            f(y) = y^(f-1)/(2 m^f K(1/(s m),abs(f)))
            exp(-((y - m)^2/(2 y s^2 m^2)))

     where m is the mean of the distribution, s the disper-
     sion, f is the family parameter, and K() is the frac-
     tional Bessel function of the third kind.

     f=-1/2 yields an inverse Gaussian distribution,
     s=infinity, f>0 a gamma distribution, and f=0 a hyper-
     bola distribution.

_U_s_a_g_e_:

     dginvgauss(y, m, s, f)
     pginvgauss(q, m, s, f)

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

       y: vector of responses.

       q: vector of quantiles.

       m: vector of means.

       s: vector of dispersion parameters.

       f: vector of family parameters.

_A_u_t_h_o_r_(_s_)_:

     J.K. Lindsey

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

     `dinvgauss' for the inverse Gaussian distribution.

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

     dginvgauss(10, 3, 1, 1)
     pginvgauss(10, 3, 1, 1)

