Generalized Inverse Gaussian     package:rmutil     R Documentation

_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 generalized inverse
     Gaussian distribution with mean equal to 'm', dispersion equal to
     's', and family parameter equal to 'f': density, cumulative
     distribution, quantiles, log hazard, and random generation.

     The generalized inverse Gaussian distribution has density

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

     where m is the mean of the distribution, s the dispersion, f is
     the family parameter, and K() is the fractional 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 hyperbola distribution.

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

     dginvgauss(y, m, s, f, log=FALSE)
     pginvgauss(q, m, s, f)
     qginvgauss(p, m, s, f)
     hginvgauss(y, m, s, f)
     rginvgauss(n, m, s, f)

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

       y: vector of responses.

       q: vector of quantiles.

       p: vector of probabilities

       n: number of values to generate

       m: vector of means.

       s: vector of dispersion parameters.

       f: vector of family parameters.

     log: if TRUE, log probabilities are supplied.

_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)
     qginvgauss(0.4, 3, 1, 1)
     rginvgauss(10, 3, 1, 1)

