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| <div class="titlepage"><div><div><h2 class="title" style="clear: both"> |
| <a name="math_toolkit.refs"></a><a class="link" href="refs.html" title="References">References</a> |
| </h2></div></div></div> |
| <h5> |
| <a name="math_toolkit.refs.h0"></a> |
| <span class="phrase"><a name="math_toolkit.refs.general_references"></a></span><a class="link" href="refs.html#math_toolkit.refs.general_references">General |
| references</a> |
| </h5> |
| <p> |
| (Specific detailed sources for individual functions and distributions are given |
| at the end of each individual section). |
| </p> |
| <p> |
| <a href="http://dlmf.nist.gov/" target="_top">DLMF (NIST Digital Library of Mathematical |
| Functions)</a> is a replacement for the legendary Abramowitz and Stegun's |
| Handbook of Mathematical Functions (often called simply A&S), |
| </p> |
| <p> |
| M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical Functions |
| with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards |
| Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C. |
| </p> |
| <p> |
| NIST Handbook of Mathematical Functions Edited by: Frank W. J. Olver, University |
| of Maryland and National Institute of Standards and Technology, Maryland, Daniel |
| W. Lozier, National Institute of Standards and Technology, Maryland, Ronald |
| F. Boisvert, National Institute of Standards and Technology, Maryland, Charles |
| W. Clark, National Institute of Standards and Technology, Maryland and University |
| of Maryland. |
| </p> |
| <p> |
| ISBN: 978-0521140638 (paperback), 9780521192255 (hardback), July 2010, Cambridge |
| University Press. |
| </p> |
| <p> |
| <a href="http://www.itl.nist.gov/div898/handbook/index.htm" target="_top">NIST/SEMATECH |
| e-Handbook of Statistical Methods</a> |
| </p> |
| <p> |
| <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html" target="_top">Mathematica |
| Documentation: DiscreteDistributions</a> The Wolfram Research Documentation |
| Center is a collection of online reference materials about Mathematica, CalculationCenter, |
| and other Wolfram Research products. |
| </p> |
| <p> |
| <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/ContinuousDistributions.html" target="_top">Mathematica |
| Documentation: ContinuousDistributions</a> The Wolfram Research Documentation |
| Center is a collection of online reference materials about Mathematica, CalculationCenter, |
| and other Wolfram Research products. |
| </p> |
| <p> |
| Statistical Distributions (Wiley Series in Probability & Statistics) (Paperback) |
| by N.A.J. Hastings, Brian Peacock, Merran Evans, ISBN: 0471371246, Wiley 2000. |
| </p> |
| <p> |
| <a href="http://www.worldscibooks.com/mathematics/p191.html" target="_top">Extreme Value |
| Distributions, Theory and Applications</a> Samuel Kotz & Saralees Nadarajah, |
| ISBN 978-1-86094-224-2 & 1-86094-224-5 Oct 2000, Chapter 1.2 discusses |
| the various extreme value distributions. |
| </p> |
| <p> |
| <a href="http://bh0.physics.ubc.ca/People/matt/Doc/ThesesOthers/Phd/pugh.pdf" target="_top">pugh.pdf |
| (application/pdf Object)</a> Pugh Msc Thesis on the Lanczos approximation |
| to the gamma function. |
| </p> |
| <p> |
| <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003" target="_top">N1514, |
| 03-0097, A Proposal to Add Mathematical Special Functions to the C++ Standard |
| Library (version 2), Walter E. Brown</a> |
| </p> |
| <h5> |
| <a name="math_toolkit.refs.h1"></a> |
| <span class="phrase"><a name="math_toolkit.refs.calculators"></a></span><a class="link" href="refs.html#math_toolkit.refs.calculators">Calculators</a> |
| </h5> |
| <p> |
| We found (and used to create cross-check spot values - as far as their accuracy |
| allowed). |
| </p> |
| <p> |
| <a href="http://functions.wolfram.com/" target="_top">The Wolfram Functions Site</a> |
| The Wolfram Functions Site - Providing the mathematical and scientific community |
| with the world's largest (and most authorititive) collection of formulas and |
| graphics about mathematical functions. |
| </p> |
| <p> |
| <a href="http://www.moshier.net/cephes28.zip" target="_top">100-decimal digit calculator</a> |
| provided some spot values. |
| </p> |
| <p> |
| <a href="http://www.adsciengineering.com/bpdcalc/" target="_top">http://www.adsciengineering.com/bpdcalc/</a> |
| Binomial Probability Distribution Calculator. |
| </p> |
| <h5> |
| <a name="math_toolkit.refs.h2"></a> |
| <span class="phrase"><a name="math_toolkit.refs.other_libraries"></a></span><a class="link" href="refs.html#math_toolkit.refs.other_libraries">Other |
| Libraries</a> |
| </h5> |
| <p> |
| <a href="http://www.moshier.net/#Cephes" target="_top">Cephes library</a> by Shephen |
| Moshier and his book: |
| </p> |
| <p> |
| Methods and programs for mathematical functions, Stephen L B Moshier, Ellis |
| Horwood (1989) ISBN 0745802893 0470216093 provided inspiration. |
| </p> |
| <p> |
| <a href="http://lib.stat.cmu.edu/general/cdflib" target="_top">CDFLIB Library of Fortran |
| Routines for Cumulative Distribution functions.</a> |
| </p> |
| <p> |
| <a href="http://www.csit.fsu.edu/~burkardt/cpp_src/dcdflib/dcdflib.html" target="_top">DCFLIB |
| C++ version</a>. |
| </p> |
| <p> |
| <a href="http://www.csit.fsu.edu/~burkardt/f_src/dcdflib/dcdflib.html" target="_top">DCDFLIB |
| C++ version</a> DCDFLIB is a library of C++ routines, using double precision |
| arithmetic, for evaluating cumulative probability density functions. |
| </p> |
| <p> |
| <a href="http://www.softintegration.com/docs/package/chnagstat/" target="_top">http://www.softintegration.com/docs/package/chnagstat/</a> |
| </p> |
| <p> |
| <a href="http://www.nag.com/numeric/numerical_libraries.asp" target="_top">NAG</a> |
| libraries. |
| </p> |
| <p> |
| <a href="http://www.mathcad.com" target="_top">MathCAD</a> |
| </p> |
| <p> |
| <a href="http://www.vni.com/products/imsl/jmsl/v30/api/com/imsl/stat/Cdf.html" target="_top">JMSL |
| Numerical Library</a> (Java). |
| </p> |
| <p> |
| John F Hart, Computer Approximations, (1978) ISBN 0 088275 642-7. |
| </p> |
| <p> |
| William J Cody, Software Manual for the Elementary Functions, Prentice-Hall |
| (1980) ISBN 0138220646. |
| </p> |
| <p> |
| Nico Temme, Special Functions, An Introduction to the Classical Functions of |
| Mathematical Physics, Wiley, ISBN: 0471-11313-1 (1996) who also gave valueable |
| advice. |
| </p> |
| <p> |
| <a href="http://www.cas.lancs.ac.uk/glossary_v1.1/prob.html#probdistn" target="_top">Statistics |
| Glossary</a>, Valerie Easton and John H. McColl. |
| </p> |
| <p> |
| <span class="underline">_R</span> R Development Core Team (2010). R: |
| A language and environment for statistical computing. R Foundation for Statistical |
| Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org. |
| </p> |
| <p> |
| For use of R, see: |
| </p> |
| <p> |
| Jim Albert, Bayesian Computation with R, ISBN 978-0-387-71384-7. |
| </p> |
| <p> |
| <a href="http://www.quantnet.com/cplusplus-statistical-distributions-boost" target="_top">C++ |
| Statistical Distributions in Boost - QuantNetwork forum</a> discusses using |
| Boost.Math in finance. |
| </p> |
| <p> |
| <a href="http://www.quantnet.com/boost-and-computational-finance/" target="_top">Quantnet |
| Boost and computational finance</a>. Robert Demming & Daniel J. Duffy, |
| Introduction to the C++ Boost Libraries - Volume I - Foundations and Volume |
| II ISBN 978-94-91028-01-4, Advanced Libraries and Applications, ISBN 978-94-91028-02-1 |
| (to be published in 2011). discusses application of Boost.Math, especially |
| in finance. |
| </p> |
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| Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert |
| Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, |
| Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
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