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Update to Owens for extra formula and reference, and to roadmap

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[SVN r78134]
This commit is contained in:
Paul A. Bristow
2012-04-22 11:45:33 +00:00
parent 73bd07a44d
commit 39ef91ac9d
2 changed files with 21 additions and 6 deletions
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25
doc/sf_and_dist/owens_t.qbk
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@@ -51,9 +51,21 @@ multivariate normal distribution probabilities.
The return type of this function is computed using the __arg_pomotion_rules:
the result is of type `double` when T is an integer type, and type T otherwise.
Owen's original paper (page 1077) provides some additional corner cases.
__spaces T(h, 0) = 0
__spaces T(0, a) = 1/2[pi] arctan(a)
__spaces T(h, 1) = [frac12] G(h) \[1 - G(h)\]
where G(h) is the univariate normal with zero mean and unit variance integral from -[infin] to h.
Owen's expressions for infinity are not yet implemented.
[h4 Accuracy]
The Patefield-Tandy algorithm provides six methods of evalualution;
The Patefield-Tandy algorithm provides six methods of evalualution (T1 to T6);
the best method is selected according to the values of ['a] and ['h].
See the original paper and the source in
[@../../../../../boost/math/special_functions/owens_t.hpp owens_t.hpp] for details.
@@ -72,7 +84,8 @@ but the real problems come when h gets large.
[h4 Testing]
Test data was generated by T1 and T4.
Test data was generated by Patefield and Tandy algorithms T1 and T4,
and also the suggested reference routine T7.
* T1 was rejected if the result was too small compared to `atan(a)` (ie cancellation),
* T4 was rejected if there was no convergence,
@@ -85,13 +98,15 @@ However, that there was a whole domain (large ['h], small ['a])
where it was not possible to generate any reliable test values
(all the methods got rejected for one reason or another).
There are also two sets of sanity tests: spot values are computed using __Mathematica and ???? TODO.
There are also two sets of sanity tests: spot values are computed using __Mathematica and __R.
[h4 Implementation]
The function was proposed and evaluated by
D. B. Owen, Tables for computing bivariate normal probabilities,
Ann. Math. Statist., 27, 1075-1090 (1956).
[@http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoms/1177728074
Donald. B. Owen, Tables for computing bivariate normal probabilities,
Ann. Math. Statist., 27, 1075-1090 (1956)].
The algorithms of Patefield, M. and Tandy, D.
"Fast and accurate Calculation of Owen's T-Function", Journal of Statistical Software, 5 (5), 1 - 25 (2000)

2
doc/sf_and_dist/roadmap.qbk
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@@ -6,7 +6,7 @@
* Promoted math constants to be 1st class citizens,
including convenient access to the most widely used
built-in float, double, long double via three namespaces.
* Added the Skew Normal distribution written by Benjamin Sobotta.
* Added the Owen's T function and Skew Normal distribution written by Benjamin Sobotta.
* Corrected issue [@https://svn.boost.org/trac/boost/ticket/6627 #6627 nonfinite_num_put formatting of 0.0 is incorrect]
based on a patch submitted by K R Walker.