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Improved docs and tests and graphs.
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pabristow
@@ -19,6 +19,7 @@
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public:
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typedef RealType value_type;
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typedef Policy policy_type;
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// Constructor from two range parameters, x_min and x_max:
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arcsine_distribution(RealType x_min, RealType x_max);
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@@ -51,13 +52,11 @@ The [@http://en.wikipedia.org/wiki/Probability_density_function probability dens
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for the [@http://en.wikipedia.org/wiki/arcsine_distribution arcsine distribution]
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defined on the interval \[0,1\] is given by:
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[sixemspace] f(x; x_min, x_max) = 1 / [pi] [sqrt]((x - x_min) (x_max - x))
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[figspace] f(x; x_min, x_max) = 1 / [pi] [sqrt]((x - x_min) (x_max - x))
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[figspace] [figspace] f(x; x_min, x_max) = 1 /([pi][sdot][sqrt]((x - x_min)[sdot](x_max - x))
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For example, __WolframAlpha arcsine distribution, from input of
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N[pDF[arcsinedistribution[0, 1], 0.5], 50]
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N[PDF[arcsinedistribution[0, 1], 0.5], 50]
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computes the PDF value
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@@ -78,7 +77,7 @@ and some generalized examples with other ['x] ranges.
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The Cumulative Distribution Function CDF is defined as
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[sixemspace] F(x) = 2 / [pi] arcsin (sqrt((x-x_min)(x_max - x)))
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[figspace] [figspace] F(x) = 2[sdot]arcsin([sqrt]((x-x_min)/(x_max - x))) / [pi]
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[graph arcsine_cdf]
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@@ -121,7 +120,7 @@ that are generic to all distributions are supported: __usual_accessors.
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The formulae for calculating these are shown in the table below, and at
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[@http://mathworld.wolfram.com/arcsineDistribution.html Wolfram Mathworld].
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[note There are always [*two] values for the mode, at ['x_min] and at ['x_max], default 0 and 1,
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[note There are always [*two] values for the [*mode], at ['x_min] and at ['x_max], default 0 and 1,
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so instead we raise the exception __domain_error.
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At these extrema, the PDFs are infinite, and the CDFs zero or unity.]
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@@ -151,14 +150,14 @@ and the PDF can be calculated thus:
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[arcsine_snip_2]
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From the plot of PDF, it is clear that ['x] = 1/2 is the [*minimum] of the curve,
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From the plot of PDF, it is clear that ['x] = [frac12] is the [*minimum] of the curve,
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so this is the [*least likely] scenario.
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(This is highly counter-intuitive, considering that fair tosses must [*eventually] become equal.
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It turns out that ['eventually] is not just very long, but infinite).
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It turns out that ['eventually] is not just very long, but [*infinite]!).
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The [*most likely] scenarios are towards the extrema where ['x] = 0 or ['x] = 1.
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If fraction of time is on the left is a 1/4,
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If fraction of time on the left is a [frac14],
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it is only slightly more likely because the curve is quite flat bottomed.
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[arcsine_snip_3]
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@@ -173,7 +172,7 @@ We can easily compute this setting ['x] = 5./100 = 0.05
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Similarly, we can compute from a fraction of 0.05 /2 = 0.025
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(halved because we are considering both winners and losers)
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corresponding to 1 - 0.025 or 97.5% of the gamblers, (walkers, particles) on the [*same side] of the origin
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corresponding to 1 - 0.025 or 97.5% of the gamblers, (walkers, particles...) on the [*same side] of the origin
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[arcsine_snip_5]
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@@ -197,7 +196,7 @@ and gamblers continue to provide proof.
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[*Moral]: if you in a losing patch, leave the game.
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(Because the odds to recover to a good patch are poor).
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[*Corollary]: Quit while you are ahead!
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[*Corollary]: Quit while you are ahead?
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A working example is at [@../../example/arcsine_example.cpp arcsine_example.cpp]
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including sample output .
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@@ -217,7 +216,7 @@ For example, for a standard [0, 1] arcsine distribution ['as], the pdf is symmet
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so that one would expect `pdf(as, 0.01) == pdf(as, 0.99)`. But as ['x] nears unity, there is increasing
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[@http://en.wikipedia.org/wiki/Loss_of_significance loss of significance].
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To counteract this, the complement versions of CDF and quantile
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are implemented with alternative expressions using ['cos[super -1]] instead of ['asin[super -1]].
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are implemented with alternative expressions using ['cos[super -1]] instead of ['sin[super -1]].
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Users should see __why_complements for guidance on when to avoid loss of accuracy by using complements.
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[h4 Testing]
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@@ -233,7 +232,7 @@ In the following table ['a] and ['b] are the parameters ['x_min][space] and ['x_
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[table
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[[Function][Implementation Notes]]
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[[support] [x [isin] \[x_min, x_max\], default x [isin] \[0, 1\] ]]
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[[support] [x [isin] \[a, b\], default x [isin] \[0, 1\] ]]
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[[pdf] [f(x; a, b) = 1/([pi][sdot][sqrt](x - a)[sdot](b - x))]]
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[[cdf] [F(x) = 2/[pi][sdot]sin[super-1]([sqrt](x - a) / (b - a) ) ]]
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[[cdf of complement] [2/([pi][sdot]cos[super-1]([sqrt](x - a) / (b - a)))]]
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@@ -101,7 +101,7 @@ public:
|
||||
double margin = 1e-2; // Margin of 1% (say) to get lowest off the 'end stop'.
|
||||
if((a != 0) && (fabs(a) > margin))
|
||||
{
|
||||
mod = a * (1 + (a > 0) ? margin : -margin));
|
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mod = a * (1 + ((a > 0) ? margin : -margin));
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||||
}
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else
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||||
{ // Case of mod near zero?
|
||||
|
||||
@@ -111,7 +111,7 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"><p><small>Last revised: October 20, 2014 at 13:16:35 GMT</small></p></td>
|
||||
<td align="left"><p><small>Last revised: November 27, 2014 at 14:58:32 GMT</small></p></td>
|
||||
<td align="right"><div class="copyright-footer"></div></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
|
||||
@@ -24,7 +24,7 @@
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1540283"></a>Function Index</h2></div></div></div>
|
||||
<a name="id1550233"></a>Function Index</h2></div></div></div>
|
||||
<p><a class="link" href="s01.html#idx_id_0">A</a> <a class="link" href="s01.html#idx_id_1">B</a> <a class="link" href="s01.html#idx_id_2">C</a> <a class="link" href="s01.html#idx_id_3">D</a> <a class="link" href="s01.html#idx_id_4">E</a> <a class="link" href="s01.html#idx_id_5">F</a> <a class="link" href="s01.html#idx_id_6">G</a> <a class="link" href="s01.html#idx_id_7">H</a> <a class="link" href="s01.html#idx_id_8">I</a> <a class="link" href="s01.html#idx_id_9">J</a> <a class="link" href="s01.html#idx_id_10">K</a> <a class="link" href="s01.html#idx_id_11">L</a> <a class="link" href="s01.html#idx_id_12">M</a> <a class="link" href="s01.html#idx_id_13">N</a> <a class="link" href="s01.html#idx_id_14">O</a> <a class="link" href="s01.html#idx_id_15">P</a> <a class="link" href="s01.html#idx_id_16">Q</a> <a class="link" href="s01.html#idx_id_17">R</a> <a class="link" href="s01.html#idx_id_18">S</a> <a class="link" href="s01.html#idx_id_19">T</a> <a class="link" href="s01.html#idx_id_20">U</a> <a class="link" href="s01.html#idx_id_21">V</a> <a class="link" href="s01.html#idx_id_23">Z</a></p>
|
||||
<div class="variablelist"><dl class="variablelist">
|
||||
<dt>
|
||||
|
||||
@@ -24,7 +24,7 @@
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1558149"></a>Class Index</h2></div></div></div>
|
||||
<a name="id1570794"></a>Class Index</h2></div></div></div>
|
||||
<p><a class="link" href="s02.html#idx_id_24">A</a> <a class="link" href="s02.html#idx_id_25">B</a> <a class="link" href="s02.html#idx_id_26">C</a> <a class="link" href="s02.html#idx_id_27">D</a> <a class="link" href="s02.html#idx_id_28">E</a> <a class="link" href="s02.html#idx_id_29">F</a> <a class="link" href="s02.html#idx_id_30">G</a> <a class="link" href="s02.html#idx_id_31">H</a> <a class="link" href="s02.html#idx_id_32">I</a> <a class="link" href="s02.html#idx_id_35">L</a> <a class="link" href="s02.html#idx_id_36">M</a> <a class="link" href="s02.html#idx_id_37">N</a> <a class="link" href="s02.html#idx_id_38">O</a> <a class="link" href="s02.html#idx_id_39">P</a> <a class="link" href="s02.html#idx_id_40">Q</a> <a class="link" href="s02.html#idx_id_41">R</a> <a class="link" href="s02.html#idx_id_42">S</a> <a class="link" href="s02.html#idx_id_43">T</a> <a class="link" href="s02.html#idx_id_44">U</a> <a class="link" href="s02.html#idx_id_46">W</a></p>
|
||||
<div class="variablelist"><dl class="variablelist">
|
||||
<dt>
|
||||
|
||||
@@ -24,7 +24,7 @@
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1559245"></a>Typedef Index</h2></div></div></div>
|
||||
<a name="id1572386"></a>Typedef Index</h2></div></div></div>
|
||||
<p><a class="link" href="s03.html#idx_id_48">A</a> <a class="link" href="s03.html#idx_id_49">B</a> <a class="link" href="s03.html#idx_id_50">C</a> <a class="link" href="s03.html#idx_id_51">D</a> <a class="link" href="s03.html#idx_id_52">E</a> <a class="link" href="s03.html#idx_id_53">F</a> <a class="link" href="s03.html#idx_id_54">G</a> <a class="link" href="s03.html#idx_id_55">H</a> <a class="link" href="s03.html#idx_id_56">I</a> <a class="link" href="s03.html#idx_id_59">L</a> <a class="link" href="s03.html#idx_id_61">N</a> <a class="link" href="s03.html#idx_id_62">O</a> <a class="link" href="s03.html#idx_id_63">P</a> <a class="link" href="s03.html#idx_id_65">R</a> <a class="link" href="s03.html#idx_id_66">S</a> <a class="link" href="s03.html#idx_id_67">T</a> <a class="link" href="s03.html#idx_id_68">U</a> <a class="link" href="s03.html#idx_id_69">V</a> <a class="link" href="s03.html#idx_id_70">W</a></p>
|
||||
<div class="variablelist"><dl class="variablelist">
|
||||
<dt>
|
||||
|
||||
@@ -24,7 +24,7 @@
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1563369"></a>Macro Index</h2></div></div></div>
|
||||
<a name="id1576499"></a>Macro Index</h2></div></div></div>
|
||||
<p><a class="link" href="s04.html#idx_id_73">B</a> <a class="link" href="s04.html#idx_id_77">F</a></p>
|
||||
<div class="variablelist"><dl class="variablelist">
|
||||
<dt>
|
||||
|
||||
@@ -23,7 +23,7 @@
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1566631"></a>Index</h2></div></div></div>
|
||||
<a name="id1577831"></a>Index</h2></div></div></div>
|
||||
<p><a class="link" href="s05.html#idx_id_96">A</a> <a class="link" href="s05.html#idx_id_97">B</a> <a class="link" href="s05.html#idx_id_98">C</a> <a class="link" href="s05.html#idx_id_99">D</a> <a class="link" href="s05.html#idx_id_100">E</a> <a class="link" href="s05.html#idx_id_101">F</a> <a class="link" href="s05.html#idx_id_102">G</a> <a class="link" href="s05.html#idx_id_103">H</a> <a class="link" href="s05.html#idx_id_104">I</a> <a class="link" href="s05.html#idx_id_105">J</a> <a class="link" href="s05.html#idx_id_106">K</a> <a class="link" href="s05.html#idx_id_107">L</a> <a class="link" href="s05.html#idx_id_108">M</a> <a class="link" href="s05.html#idx_id_109">N</a> <a class="link" href="s05.html#idx_id_110">O</a> <a class="link" href="s05.html#idx_id_111">P</a> <a class="link" href="s05.html#idx_id_112">Q</a> <a class="link" href="s05.html#idx_id_113">R</a> <a class="link" href="s05.html#idx_id_114">S</a> <a class="link" href="s05.html#idx_id_115">T</a> <a class="link" href="s05.html#idx_id_116">U</a> <a class="link" href="s05.html#idx_id_117">V</a> <a class="link" href="s05.html#idx_id_118">W</a> <a class="link" href="s05.html#idx_id_119">Z</a></p>
|
||||
<div class="variablelist"><dl class="variablelist">
|
||||
<dt>
|
||||
|
||||
@@ -27,7 +27,7 @@
|
||||
<a name="math_toolkit.conventions"></a><a class="link" href="conventions.html" title="Document Conventions">Document Conventions</a>
|
||||
</h2></div></div></div>
|
||||
<p>
|
||||
<a class="indexterm" name="id898684"></a>
|
||||
<a class="indexterm" name="id908244"></a>
|
||||
</p>
|
||||
<p>
|
||||
This documentation aims to use of the following naming and formatting conventions.
|
||||
|
||||
@@ -27,7 +27,7 @@
|
||||
<a name="math_toolkit.navigation"></a><a class="link" href="navigation.html" title="Navigation">Navigation</a>
|
||||
</h2></div></div></div>
|
||||
<p>
|
||||
<a class="indexterm" name="id898599"></a>
|
||||
<a class="indexterm" name="id908135"></a>
|
||||
</p>
|
||||
<p>
|
||||
Boost.Math documentation is provided in both HTML and PDF formats.
|
||||
|
||||
@@ -710,7 +710,20 @@
|
||||
/cygdrive/c/progra~1/Inkscape/inkscape -d 120 -e $(cygpath -a -w $(basename $file .svg).png) $(cygpath -a -w $file);
|
||||
done</pre>
|
||||
<p>
|
||||
Currently Inkscape seems to generate the better looking png's.
|
||||
Using BASH
|
||||
</p>
|
||||
<pre class="programlisting"># Convert single SVG to PNG file.
|
||||
# /c/progra~1/Inkscape/inkscape -d 120 -e a.png a.svg
|
||||
</pre>
|
||||
<p>
|
||||
or to convert All files in folder SVG to PNG.
|
||||
</p>
|
||||
<pre class="programlisting">for file in *.svg; do
|
||||
/c/progra~1/Inkscape/inkscape -d 120 -e $(basename $file .svg).png $file
|
||||
done
|
||||
</pre>
|
||||
<p>
|
||||
Currently Inkscape seems to generate the better looking PNGs.
|
||||
</p>
|
||||
<p>
|
||||
The PDF is generated into \pdf\math.pdf using a command from a shell or command
|
||||
|
||||
@@ -90,11 +90,10 @@ namespace boost
|
||||
function,
|
||||
msg.c_str(), x_max, pol);
|
||||
// "x_max argument is %1%, but must be > x_min !", x_max, pol);
|
||||
// "x_max argument is %1%, but must be > x_min %2!", x_max, x_min, pol); would be better. TODO?
|
||||
// "x_max argument is %1%, but must be > x_min %2!", x_max, x_min, pol); would be better.
|
||||
// But would require replication of all helpers functions in /policies/error_handling.hpp for two values,
|
||||
// as well as two value versions of raise_error, raise_domain_error and do_format ...
|
||||
|
||||
|
||||
// so use slightly hacky lexical_cast to string instead.
|
||||
return false;
|
||||
}
|
||||
return true;
|
||||
@@ -208,22 +207,44 @@ namespace boost
|
||||
inline const std::pair<RealType, RealType> support(const arcsine_distribution<RealType, Policy>& dist)
|
||||
{ // Range of supported values for random variable x.
|
||||
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
|
||||
|
||||
return std::pair<RealType, RealType>(static_cast<RealType>(dist.x_min()), static_cast<RealType>(dist.x_max()));
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType mean(const arcsine_distribution<RealType, Policy>& dist)
|
||||
{ // Mean of arcsine distribution .
|
||||
return (dist.x_min() + dist.x_max()) / 2;
|
||||
RealType result;
|
||||
RealType x_min = dist.x_min();
|
||||
RealType x_max = dist.x_max();
|
||||
|
||||
if (false == arcsine_detail::check_dist(
|
||||
"boost::math::mean(arcsine_distribution<%1%> const&, %1% )",
|
||||
x_min,
|
||||
x_max,
|
||||
&result, Policy())
|
||||
)
|
||||
{
|
||||
return result;
|
||||
}
|
||||
return (x_min + x_max) / 2;
|
||||
} // mean
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType variance(const arcsine_distribution<RealType, Policy>& dist)
|
||||
{ // Variance of standard arcsine distribution = (1-0)/8 = 0.125.
|
||||
RealType a = dist.x_min();
|
||||
RealType b = dist.x_max();
|
||||
return (b - a) * (b - a) / 8;
|
||||
RealType result;
|
||||
RealType x_min = dist.x_min();
|
||||
RealType x_max = dist.x_max();
|
||||
if (false == arcsine_detail::check_dist(
|
||||
"boost::math::variance(arcsine_distribution<%1%> const&, %1% )",
|
||||
x_min,
|
||||
x_max,
|
||||
&result, Policy())
|
||||
)
|
||||
{
|
||||
return result;
|
||||
}
|
||||
return (x_max - x_min) * (x_max - x_min) / 8;
|
||||
} // variance
|
||||
|
||||
template <class RealType, class Policy>
|
||||
@@ -240,25 +261,77 @@ namespace boost
|
||||
template <class RealType, class Policy>
|
||||
inline RealType median(const arcsine_distribution<RealType, Policy>& dist)
|
||||
{ // Median of arcsine distribution (a + b) / 2 == mean.
|
||||
return (dist.x_min() + dist.x_max()) / 2;
|
||||
RealType x_min = dist.x_min();
|
||||
RealType x_max = dist.x_max();
|
||||
RealType result;
|
||||
if (false == arcsine_detail::check_dist(
|
||||
"boost::math::median(arcsine_distribution<%1%> const&, %1% )",
|
||||
x_min,
|
||||
x_max,
|
||||
&result, Policy())
|
||||
)
|
||||
{
|
||||
return result;
|
||||
}
|
||||
return (x_min + x_max) / 2;
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType skewness(const arcsine_distribution<RealType, Policy>& /* dist */)
|
||||
inline RealType skewness(const arcsine_distribution<RealType, Policy>& dist)
|
||||
{
|
||||
RealType result;
|
||||
RealType x_min = dist.x_min();
|
||||
RealType x_max = dist.x_max();
|
||||
|
||||
if (false == arcsine_detail::check_dist(
|
||||
"boost::math::skewness(arcsine_distribution<%1%> const&, %1% )",
|
||||
x_min,
|
||||
x_max,
|
||||
&result, Policy())
|
||||
)
|
||||
{
|
||||
return result;
|
||||
}
|
||||
return 0;
|
||||
} // skewness
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType kurtosis_excess(const arcsine_distribution<RealType, Policy>& /* dist */)
|
||||
inline RealType kurtosis_excess(const arcsine_distribution<RealType, Policy>& dist)
|
||||
{
|
||||
RealType result = -3;
|
||||
RealType result;
|
||||
RealType x_min = dist.x_min();
|
||||
RealType x_max = dist.x_max();
|
||||
|
||||
if (false == arcsine_detail::check_dist(
|
||||
"boost::math::kurtosis_excess(arcsine_distribution<%1%> const&, %1% )",
|
||||
x_min,
|
||||
x_max,
|
||||
&result, Policy())
|
||||
)
|
||||
{
|
||||
return result;
|
||||
}
|
||||
result = -3;
|
||||
return result / 2;
|
||||
} // kurtosis_excess
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType kurtosis(const arcsine_distribution<RealType, Policy>& dist)
|
||||
{
|
||||
RealType result;
|
||||
RealType x_min = dist.x_min();
|
||||
RealType x_max = dist.x_max();
|
||||
|
||||
if (false == arcsine_detail::check_dist(
|
||||
"boost::math::kurtosis(arcsine_distribution<%1%> const&, %1% )",
|
||||
x_min,
|
||||
x_max,
|
||||
&result, Policy())
|
||||
)
|
||||
{
|
||||
return result;
|
||||
}
|
||||
|
||||
return 3 + kurtosis_excess(dist);
|
||||
} // kurtosis
|
||||
|
||||
@@ -275,7 +348,7 @@ namespace boost
|
||||
RealType x = xx;
|
||||
|
||||
// Argument checks:
|
||||
RealType result = 0;
|
||||
RealType result = 0;
|
||||
if (false == arcsine_detail::check_dist_and_x(
|
||||
function,
|
||||
lo, hi, x,
|
||||
|
||||
@@ -41,35 +41,183 @@ using std::endl;
|
||||
#include <limits>
|
||||
using std::numeric_limits;
|
||||
|
||||
|
||||
template <class RealType>
|
||||
void test_ignore_policy(RealType)
|
||||
{
|
||||
// Check on returns when errors are ignored.
|
||||
if ((typeid(RealType) != typeid(boost::math::concepts::real_concept))
|
||||
&& std::numeric_limits<RealType>::has_infinity
|
||||
&& std::numeric_limits<RealType>::has_quiet_NaN
|
||||
)
|
||||
{ // Ordinary floats only.
|
||||
|
||||
using namespace boost::math;
|
||||
// RealType inf = std::numeric_limits<RealType>::infinity();
|
||||
RealType nan = std::numeric_limits<RealType>::quiet_NaN();
|
||||
|
||||
using boost::math::policies::policy;
|
||||
// Types of error whose action can be altered by policies:.
|
||||
//using boost::math::policies::evaluation_error;
|
||||
//using boost::math::policies::domain_error;
|
||||
//using boost::math::policies::overflow_error;
|
||||
//using boost::math::policies::underflow_error;
|
||||
//using boost::math::policies::domain_error;
|
||||
//using boost::math::policies::pole_error;
|
||||
|
||||
//// Actions on error (in enum error_policy_type):
|
||||
//using boost::math::policies::errno_on_error;
|
||||
//using boost::math::policies::ignore_error;
|
||||
//using boost::math::policies::throw_on_error;
|
||||
//using boost::math::policies::denorm_error;
|
||||
//using boost::math::policies::pole_error;
|
||||
//using boost::math::policies::user_error;
|
||||
|
||||
typedef policy<
|
||||
boost::math::policies::domain_error<boost::math::policies::ignore_error>,
|
||||
boost::math::policies::overflow_error<boost::math::policies::ignore_error>,
|
||||
boost::math::policies::underflow_error<boost::math::policies::ignore_error>,
|
||||
boost::math::policies::denorm_error<boost::math::policies::ignore_error>,
|
||||
boost::math::policies::pole_error<boost::math::policies::ignore_error>,
|
||||
boost::math::policies::evaluation_error<boost::math::policies::ignore_error>
|
||||
> ignore_all_policy;
|
||||
|
||||
typedef arcsine_distribution<RealType, ignore_all_policy> ignore_error_arcsine;
|
||||
|
||||
// Only test NaN and infinity if type has these features (realconcept returns zero).
|
||||
// Integers are always converted to RealType,
|
||||
// others requires static cast to RealType from long double.
|
||||
|
||||
if (std::numeric_limits<RealType>::has_quiet_NaN)
|
||||
{
|
||||
// PDF
|
||||
if (std::numeric_limits<RealType>::has_infinity)
|
||||
{
|
||||
// pdf(ignore_error_arcsine(0, 1), std::numeric_limits<RealType>::infinity());
|
||||
// std::cout << "arcsine(-1,+1) ignore error pdf (infinity) " << pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) << std::endl;
|
||||
// arcsine(-1,+1) ignore error pdf (infinity) 1.#QNAN
|
||||
}
|
||||
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), std::numeric_limits<RealType>::infinity()))); // x == infinity
|
||||
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), std::numeric_limits<RealType>::infinity()))); // x == infinity
|
||||
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), static_cast <RealType>(-2)))); // x < xmin
|
||||
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), static_cast <RealType>(-2)))); // x < xmin
|
||||
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), static_cast <RealType>(+2)))); // x > x_max
|
||||
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), static_cast <RealType>(+2)))); // x > x_max
|
||||
|
||||
// Mean
|
||||
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(-nan, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(+nan, 0))));
|
||||
|
||||
if (std::numeric_limits<RealType>::has_infinity)
|
||||
{
|
||||
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(-std::numeric_limits<RealType>::infinity(), 0))));
|
||||
// std::cout << "arcsine(-inf,+1) mean " << mean(ignore_error_arcsine(-std::numeric_limits<RealType>::infinity())) << std::endl;
|
||||
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(std::numeric_limits<RealType>::infinity(), 0))));
|
||||
}
|
||||
// Check error message is correct.
|
||||
try
|
||||
{
|
||||
typedef arcsine_distribution<RealType> signal_error_arcsine;
|
||||
//std::cout << mean(signal_error_arcsine(-std::numeric_limits<RealType>::infinity())) << std::endl;
|
||||
// Error in function boost::math::arcsine_distribution<float>::arcsine_distribution: x_min argument is -1.#INF, but must be finite !
|
||||
}
|
||||
catch (std::exception ex)
|
||||
{
|
||||
std::cout << ex.what() << std::endl;
|
||||
}
|
||||
|
||||
// NaN constructors.
|
||||
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(2, nan))));
|
||||
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(nan, nan))));
|
||||
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(nan, 2))));
|
||||
|
||||
// Variance
|
||||
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(nan, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(1, nan))));
|
||||
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(2, nan))));
|
||||
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(0, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(1, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(static_cast<RealType>(1.7L), 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(2, 0))));
|
||||
|
||||
// Skewness
|
||||
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(nan, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(-1, nan))));
|
||||
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(0, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(1, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(2, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(3, 0))));
|
||||
|
||||
// Kurtosis
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(nan, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(-1, nan))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(0, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(1, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(2, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(static_cast<RealType>(2.0001L), 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(3, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(4, 0))));
|
||||
|
||||
// Kurtosis excess
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(nan, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(-1, nan))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(0, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(1, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(2, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(static_cast<RealType>(2.0001L), 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(3, 0))));
|
||||
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(4, 0))));
|
||||
} // has_quiet_NaN
|
||||
|
||||
//
|
||||
BOOST_CHECK(boost::math::isfinite(mean(ignore_error_arcsine(0, std::numeric_limits<RealType>::epsilon()))));
|
||||
|
||||
// Checks on error messages.
|
||||
try
|
||||
{
|
||||
typedef arcsine_distribution<RealType> signal_error_arcsine;
|
||||
// std::cout << "mean(ignore_error_arcsine(0, std::numeric_limits<RealType>::epsilon())) == " << std::endl;
|
||||
// std::cout << mean(ignore_error_arcsine(0, std::numeric_limits<RealType>::epsilon())) << std::endl; // 5.96046e-008
|
||||
//std::cout << "mean(ignore_error_arcsine(0, 0)) == " << std::endl;
|
||||
//std::cout << mean(ignore_error_arcsine(0, 0)) << std::endl; // 1.#QNAN
|
||||
}
|
||||
catch (std::exception ex)
|
||||
{
|
||||
std::cout << ex.what() << std::endl;
|
||||
}
|
||||
|
||||
check_support<arcsine_distribution<RealType> >(arcsine_distribution<RealType>(0, 1));
|
||||
} // ordinary floats.
|
||||
} // template <class RealType> void test_ignore_policy(RealType)
|
||||
|
||||
|
||||
template <class RealType>
|
||||
RealType informax()
|
||||
{
|
||||
{ //! \return Infinity else max_value.
|
||||
return ((std::numeric_limits<RealType>::has_infinity) ?
|
||||
std::numeric_limits<RealType>::infinity() : boost::math::tools::max_value<RealType>());
|
||||
}
|
||||
|
||||
/*
|
||||
template <class RealType>
|
||||
void test_spot(
|
||||
RealType a, // alpha a
|
||||
RealType b, // arcsine b
|
||||
RealType a, // alpha a or lo or x_min
|
||||
RealType b, // arcsine b or hi or x_maz
|
||||
RealType x, // Probability
|
||||
RealType P, // CDF of arcsine(a, b)
|
||||
RealType Q, // Complement of CDF
|
||||
RealType Q, // Complement of CDF of arcsine (a, b)
|
||||
RealType tol) // Test tolerance.
|
||||
{
|
||||
boost::math::arcsine_distribution<RealType> arcsine(a, b);
|
||||
BOOST_CHECK_CLOSE_FRACTION(cdf(aarcsine, x), P, tol);
|
||||
boost::math::arcsine_distribution<RealType> anarcsine(a, b);
|
||||
BOOST_CHECK_CLOSE_FRACTION(cdf(anarcsine, x), P, tol);
|
||||
if ((P < 0.99) && (Q < 0.99))
|
||||
{ // We can only check this if P is not too close to 1,
|
||||
{ // We can only check this if P is not too close to 1,
|
||||
// so that we can guarantee that Q is free of error,
|
||||
// (and similarly for Q)
|
||||
BOOST_CHECK_CLOSE_FRACTION(
|
||||
cdf(complement(aarcsine, x)), Q, tol);
|
||||
// (and similarly for Q).
|
||||
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(anarcsine, x)), Q, tol);
|
||||
if (x != 0)
|
||||
{
|
||||
BOOST_CHECK_CLOSE_FRACTION(
|
||||
quantile(aarcsine, P), x, tol);
|
||||
quantile(anarcsine, P), x, tol);
|
||||
}
|
||||
else
|
||||
{
|
||||
@@ -79,24 +227,23 @@ void test_spot(
|
||||
{
|
||||
// Limit where this is checked: if exponent range is very large we may
|
||||
// run out of iterations in our root finding algorithm.
|
||||
BOOST_CHECK(quantile(aarcsine, P) < boost::math::tools::epsilon<RealType>() * 10);
|
||||
BOOST_CHECK(quantile(anarcsine, P) < boost::math::tools::epsilon<RealType>() * 10);
|
||||
}
|
||||
} // if k
|
||||
if (x != 0)
|
||||
{
|
||||
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(aarcsine, Q)), x, tol);
|
||||
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(anarcsine, Q)), x, tol);
|
||||
}
|
||||
else
|
||||
{ // Just check quantile is very small:
|
||||
if ((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
|
||||
{ // Limit where this is checked: if exponent range is very large we may
|
||||
// run out of iterations in our root finding algorithm.
|
||||
BOOST_CHECK(quantile(complement(aarcsine, Q)) < boost::math::tools::epsilon<RealType>() * 10);
|
||||
BOOST_CHECK(quantile(complement(anarcsine, Q)) < boost::math::tools::epsilon<RealType>() * 10);
|
||||
}
|
||||
} // if x
|
||||
}
|
||||
} // template <class RealType> void test_spot
|
||||
*/
|
||||
|
||||
template <class RealType> // Any floating-point type RealType.
|
||||
void test_spots(RealType)
|
||||
@@ -133,8 +280,25 @@ void test_spots(RealType)
|
||||
// 0.63661977236758134307553505349005744813783858296183
|
||||
|
||||
arcsine_distribution<RealType> arcsine_01; // (Our) Standard arcsine.
|
||||
// Member functions.
|
||||
BOOST_CHECK_EQUAL(arcsine_01.x_min(), 0);
|
||||
BOOST_CHECK_EQUAL(arcsine_01.x_max(), 1);
|
||||
|
||||
// Derived functions.
|
||||
BOOST_CHECK_EQUAL(mean(arcsine_01), 0.5); // 1 / (1 + 1) = 1/2 exactly.
|
||||
BOOST_CHECK_EQUAL(median(arcsine_01), 0.5); // 1 / (1 + 1) = 1/2 exactly.
|
||||
BOOST_CHECK_EQUAL(variance(arcsine_01), 0.125); // 1/8 = 0.125
|
||||
BOOST_CHECK_CLOSE_FRACTION(standard_deviation(arcsine_01), one_div_root_two<double>() / 2, tolerance); // 1/ sqrt(s) = 0.35355339059327379
|
||||
BOOST_CHECK_EQUAL(skewness(arcsine_01), 0); //
|
||||
BOOST_CHECK_EQUAL(kurtosis_excess(arcsine_01), -1.5); // 3/2
|
||||
BOOST_CHECK_EQUAL(support(arcsine_01).first, 0); //
|
||||
BOOST_CHECK_EQUAL(range(arcsine_01).first, 0); //
|
||||
BOOST_CHECK_THROW(mode(arcsine_01), std::domain_error); // Two modes at x_min and x_max, so throw instead.
|
||||
|
||||
// PDF
|
||||
// N[PDF[arcsinedistribution[0, 1], 0.25], 50]
|
||||
// N[PDF[arcsinedistribution[0, 1], 0.75], 50]
|
||||
// 0.73510519389572273268176866441729258852984864048885
|
||||
|
||||
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.000001), static_cast<RealType>(318.31004533885312973989414360099118178698415543136L), tolerance);
|
||||
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.000005), static_cast<RealType>(142.35286456604168061345817902422241622116338936911L), tolerance);
|
||||
@@ -179,14 +343,12 @@ void test_spots(RealType)
|
||||
// Quantile.
|
||||
|
||||
// Check 1st, 2nd and 3rd quartiles.
|
||||
|
||||
// N[PDF[arcsinedistribution[0, 1], 0.25], 50]
|
||||
// 0.73510519389572273268176866441729258852984864048885
|
||||
|
||||
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.25L)), static_cast<RealType>(0.14644660940672624L), tolerance);
|
||||
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.5L)), 0.5, 2 * tolerance); // probability = 0.5, x = 0.5
|
||||
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.75L)), static_cast<RealType>(0.85355339059327373L), tolerance);
|
||||
|
||||
|
||||
|
||||
// N[CDF[arcsinedistribution[0, 1], 0.05], 50] == 0.14356629312870627075094188477505571882161519989741
|
||||
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L)), 0.05, tolerance);
|
||||
|
||||
@@ -232,6 +394,30 @@ void test_spots(RealType)
|
||||
BOOST_CHECK_SMALL(quantile(as_m11, static_cast<RealType>(0.5L)), 2 * tolerance); // p = 0.5, x = 0
|
||||
BOOST_CHECK_CLOSE_FRACTION(quantile(as_m11, static_cast<RealType>(2) / 3), +static_cast<RealType>(0.5L), 4 * tolerance); // p = 2/3, x = +0.5
|
||||
|
||||
// Loop back tests.
|
||||
test_spot(
|
||||
static_cast<RealType>(0), // lo or a
|
||||
static_cast<RealType>(1), // hi or b
|
||||
static_cast<RealType>(0.05), // Random variate x
|
||||
static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), // Probability of result (CDF of arcsine), P
|
||||
static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), // Complement of CDF Q = 1 - P
|
||||
tolerance); // Test tolerance.
|
||||
|
||||
test_spot(
|
||||
static_cast<RealType>(0), // lo or a
|
||||
static_cast<RealType>(1), // hi or b
|
||||
static_cast<RealType>(0.95), // Random variate x
|
||||
static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), // Probability of result (CDF of arcsine), P
|
||||
static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), // Complement of CDF Q = 1 - P
|
||||
tolerance * 4); // Test tolerance (slightly inceased compared to x < 0.5 above).
|
||||
|
||||
test_spot(
|
||||
static_cast<RealType>(0), // lo or a
|
||||
static_cast<RealType>(1), // hi or b
|
||||
static_cast<RealType>(static_cast<RealType>(0.5L)), // Random variate x
|
||||
static_cast<RealType>(static_cast<RealType>(0.5L)), // Probability of result (CDF of arcsine), P
|
||||
static_cast<RealType>(static_cast<RealType>(0.5L)), // Complement of CDF Q = 1 - P
|
||||
tolerance * 4); // Test tolerance.
|
||||
|
||||
// Arcsine(-2, -1) xmin = -2, x_max = -1 - Asymmetric both negative.
|
||||
arcsine_distribution<RealType> as_m2m1(-2, -1);
|
||||
@@ -265,6 +451,7 @@ void test_spots(RealType)
|
||||
BOOST_CHECK_THROW(mode(arcsine_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1))), std::domain_error);
|
||||
// mode is undefined, and must throw domain_error!
|
||||
|
||||
|
||||
BOOST_CHECK_THROW( // For various bad arguments.
|
||||
pdf(
|
||||
arcsine_distribution<RealType>(static_cast<RealType>(+1), static_cast<RealType>(-1)), // min_x > max_x
|
||||
@@ -293,8 +480,8 @@ void test_spots(RealType)
|
||||
// Checks on things that are errors.
|
||||
|
||||
// Construction with 'bad' parameters.
|
||||
BOOST_CHECK_THROW(arcsine_distribution<RealType>(+1, -1), std::domain_error);
|
||||
BOOST_CHECK_THROW(arcsine_distribution<RealType>(+1, 0), std::domain_error);
|
||||
BOOST_CHECK_THROW(arcsine_distribution<RealType>(+1, -1), std::domain_error); // max < min.
|
||||
BOOST_CHECK_THROW(arcsine_distribution<RealType>(+1, 0), std::domain_error); // max < min.
|
||||
|
||||
arcsine_distribution<> dist;
|
||||
BOOST_CHECK_THROW(pdf(dist, -1), std::domain_error);
|
||||
@@ -351,13 +538,16 @@ void test_spots(RealType)
|
||||
// Error handling checks:
|
||||
check_out_of_range<boost::math::arcsine_distribution<RealType> >(-1, +1); // (All) valid constructor parameter values.
|
||||
// and range and non-finite.
|
||||
|
||||
test_ignore_policy(static_cast<RealType>(0));
|
||||
|
||||
} // template <class RealType>void test_spots(RealType)
|
||||
|
||||
BOOST_AUTO_TEST_CASE(test_main)
|
||||
{
|
||||
BOOST_MATH_CONTROL_FP;
|
||||
|
||||
// Check that can generate arcsine distribution using one convenience methods:
|
||||
// Check that can generate arcsine distribution using convenience method:
|
||||
using boost::math::arcsine;
|
||||
|
||||
arcsine_distribution<> arcsine_01; // Using default RealType double.
|
||||
@@ -365,6 +555,7 @@ void test_spots(RealType)
|
||||
|
||||
arcsine as; // Using typedef for default standard arcsine.
|
||||
|
||||
//
|
||||
BOOST_CHECK_EQUAL(as.x_min(), 0); //
|
||||
BOOST_CHECK_EQUAL(as.x_max(), 1);
|
||||
BOOST_CHECK_EQUAL(mean(as), 0.5); // 1 / (1 + 1) = 1/2 exactly.
|
||||
@@ -376,9 +567,8 @@ void test_spots(RealType)
|
||||
BOOST_CHECK_EQUAL(support(as).first, 0); //
|
||||
BOOST_CHECK_EQUAL(range(as).first, 0); //
|
||||
BOOST_CHECK_THROW(mode(as), std::domain_error); // Two modes at x_min and x_max, so throw instead.
|
||||
// BOOST_CHECK_THROW(arcsine_distribution<double>(+1, -1), std::domain_error); // min > max
|
||||
|
||||
// (Parameter value, arbitrarily zero, only communicates the floating point type).
|
||||
// (Parameter value, arbitrarily zero, only communicates the floating point type).
|
||||
test_spots(0.0F); // Test float.
|
||||
test_spots(0.0); // Test double.
|
||||
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
||||
@@ -392,8 +582,20 @@ void test_spots(RealType)
|
||||
|
||||
/*
|
||||
|
||||
|
||||
Microsoft Visual Studio Professional 2013
|
||||
Version 12.0.30110.00 Update 1
|
||||
|
||||
1> Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_arcsine.exe"
|
||||
1> Running 1 test case...
|
||||
1> Platform: Win32
|
||||
1> Compiler: Microsoft Visual C++ version 12.0 ???? MSVC says 2013
|
||||
1> STL : Dinkumware standard library version 610
|
||||
1> Boost : 1.56.0
|
||||
|
||||
Sample Output is:
|
||||
|
||||
1> Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_arcsine.exe"
|
||||
1> Running 1 test case...
|
||||
1> Platform: Win32
|
||||
1> Compiler: Microsoft Visual C++ version 12.0
|
||||
@@ -406,7 +608,17 @@ void test_spots(RealType)
|
||||
1>
|
||||
1> *** No errors detected
|
||||
|
||||
GCC 4.9.1
|
||||
|
||||
Running 1 test case...
|
||||
tolerance = 2.38419e-007
|
||||
tolerance = 4.44089e-016
|
||||
tolerance = 4.44089e-016
|
||||
tolerance = 4.44089e-016
|
||||
|
||||
*** No errors detected
|
||||
|
||||
RUN SUCCESSFUL (total time: 141ms)
|
||||
|
||||
*/
|
||||
|
||||
|
||||
Reference in New Issue
Block a user