Igamma                  package:UCS                  R Documentation

_T_h_e _I_n_c_o_m_p_l_e_t_e _G_a_m_m_a _F_u_n_c_t_i_o_n (_s_f_u_n_c)

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

     Computes the incomplete Gamma function and its inverse.  Both the
     lower and the upper incomplete Gamma function are supported, and
     the Gamma value can be scaled to a base 10 logarithm.

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

     Igamma(a, x, lower=TRUE, log=FALSE)

     Igamma.inv(a, y, lower=TRUE, log=FALSE)

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

       a: a non-negative numeric vector, the parameter of the
          incomplete Gamma function

       x: a non-negative numeric vector, the point at which the
          incomplete Gamma function is evaluated

       y: a numeric vector, the values of the incomplete Gamma function
          (or their base 10 logarithms if 'log=TRUE')

   lower: if 'TRUE', computes the lower incomplete Gamma function
          (default).  Otherwise, computes the upper incomplete Gamma
          function.

     log: if 'TRUE', the Gamma values are base 10 logarithms (default:
          'FALSE')

_D_e_t_a_i_l_s:

     The upper incomplete Gamma function is defined by the Gamma
     integral

            Gamma(a,x) = integral_x^Inf t^(a-1) exp(-t) dt

     The lower incomplete Gamma function is defined by the
     complementary Gamma integral

             gamma(a,x) = integral_0^x t^(a-1) exp(-t) dt

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

     'Igamma' returns the (lower or upper) incomplete Gamma function
     with parameter 'a' evaluated at point 'x'.

     'Igamma.inv' returns the point 'x' at which the (lower or upper)
     incomplete Gamma function with parameter 'a' evaluates to 'y'.

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

     'Cgamma', 'Rgamma', 'Cbeta', 'Ibeta', 'Rbeta'

