statespace_special

Special functions for the p-values of the diagnostic tests.

real(dp) function gammp(a, x)       ! regularized lower incomplete gamma P(a, x)
real(dp) function gammq(a, x)       ! Q(a, x) = 1 - P(a, x), accurate in the upper tail
real(dp) function betai(a, b, x)    ! regularized incomplete beta I_x(a, b)
real(dp) function chi2_sf(x, df)    ! P(chi2(df) > x)
real(dp) function f_cdf(x, d1, d2)  ! P(F(d1, d2) <= x)

The incomplete gamma function uses its power series below \(x = a + 1\) and its continued fraction above, the incomplete beta function its continued fraction; the continued fractions are evaluated by the modified Lentz method (Thompson and Barnett 1986). The results match SciPy to 1e-12 in the tests.