[tip When people normally talk about the inverse of the incomplete
gamma function, they are talking about inverting on parameter /x/.
-These are implemented here as gamma_p_inv and gamma_q_inv, and are by
+These are implemented here as `gamma_p_inv` and `gamma_q_inv`, and are by
far the most efficient of the inverses presented here.
The inverse on the /a/ parameter finds use in some statistical
applications but has to be computed by rather brute force numerical
techniques and is consequently several times slower.
-These are implemented here as gamma_p_inva and gamma_q_inva.]
+These are implemented here as `gamma_p_inva` and `gamma_q_inva`.]
template <class T1, class T2>
[h4 Implementation]
-The functions gamma_p_inv and [@http://functions.wolfram.com/GammaBetaErf/InverseGammaRegularized/ gamma_q_inv]
+The functions `gamma_p_inv` and [@http://functions.wolfram.com/GammaBetaErf/InverseGammaRegularized/ `gamma_q_inv`]
share a common implementation.
First an initial approximation is computed using the methodology described
to produce a result as accurate as the forward incomplete gamma function, and
in many cases only one iteration is required.
-The functions gamma_p_inva and gamma_q_inva also share a common implementation
-but are handled separately from gamma_p_inv and gamma_q_inv.
+The functions `gamma_p_inva` and `gamma_q_inva` also share a common implementation
+but are handled separately from `gamma_p_inv` and `gamma_q_inv`.
An initial approximation for /a/ is computed very crudely so that
/gamma_p(a, x) ~ 0.5/, this value is then used as a starting point
for a generic derivative-free root finding algorithm. As a consequence,
these two functions are rather more expensive to compute than the
-gamma_p_inv or gamma_q_inv functions. Even so, the root is usually found
+`gamma_p_inv` or `gamma_q_inv` functions. Even so, the root is usually found
in fewer than 10 iterations.
-[endsect][/section The Incomplete Gamma Function Inverses]
+[endsect] [/section The Incomplete Gamma Function Inverses]
[/
Copyright 2006 John Maddock and Paul A. Bristow.