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From: john_at_[hidden]
Date: 2008-01-19 09:15:57

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Author: johnmaddock
Date: 2008-01-19 09:15:57 EST (Sat, 19 Jan 2008)
New Revision: 42864
URL: http://svn.boost.org/trac/boost/changeset/42864

Log:
Added non central chi squared equations.
Added:
   sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref1.mml (contents, props changed)
   sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref2.mml (contents, props changed)
   sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref3.mml (contents, props changed)
   sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref4.mml (contents, props changed)
   sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref5.mml (contents, props changed)
   sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref6.mml (contents, props changed)
   sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref7.mml (contents, props changed)

Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref1.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref1.mml 2008-01-19 09:15:57 EST (Sat, 19 Jan 2008)
@@ -0,0 +1,35 @@
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <munderover>
+ <mo>∑</mo>
+ <mrow>
+ <mi>i</mi>
+ <mo>=</mo>
+ <mn>1</mn>
+ </mrow>
+ <mi>k</mi>
+ </munderover>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>χ</mi>
+ <mi>i</mi>
+ </msub>
+ </mrow>
+ <mrow>
+ <msub>
+ <mi>σ</mi>
+ <mi>i</mi>
+ </msub>
+ </mrow>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mn>2</mn>
+ </msup>
+ </mrow>
+</math>
+

Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref2.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref2.mml 2008-01-19 09:15:57 EST (Sat, 19 Jan 2008)
@@ -0,0 +1,39 @@
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mi>λ</mi>
+ <mspace width="1em"/>
+ <mo>=</mo>
+ <mspace width="1em"/>
+ <munderover>
+ <mo>∑</mo>
+ <mrow>
+ <mi>i</mi>
+ <mo>=</mo>
+ <mn>1</mn>
+ </mrow>
+ <mi>k</mi>
+ </munderover>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>μ</mi>
+ <mi>i</mi>
+ </msub>
+ </mrow>
+ <mrow>
+ <msub>
+ <mi>σ</mi>
+ <mi>i</mi>
+ </msub>
+ </mrow>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mn>2</mn>
+ </msup>
+ </mrow>
+</math>
+

Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref3.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref3.mml 2008-01-19 09:15:57 EST (Sat, 19 Jan 2008)
@@ -0,0 +1,132 @@
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mi>f</mi>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>;</mo>
+ <mi>ν</mi>
+ <mo>,</mo>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>=</mo>
+ <mspace width="1em"/>
+ <munderover>
+ <mo>∑</mo>
+ <mrow>
+ <mi>i</mi>
+ <mo>=</mo>
+ <mn>0</mn>
+ </mrow>
+ <mi>∞</mi>
+ </munderover>
+ <mfrac>
+ <mrow>
+ <msup>
+ <mi>e</mi>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mi>i</mi>
+ </msup>
+ </mrow>
+ <mrow>
+ <mi>i</mi>
+ <mo>!</mo>
+ </mrow>
+ </mfrac>
+ <mi>f</mi>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>;</mo>
+ <mi>ν</mi>
+ <mo>+</mo>
+ <mn>2</mn>
+ <mi>i</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>=</mo>
+ <mspace width="1em"/>
+ <mfrac>
+ <mn>1</mn>
+ <mn>2</mn>
+ </mfrac>
+ <msup>
+ <mi>e</mi>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>+</mo>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mi>x</mi>
+ <mi>λ</mi>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mrow>
+ <mfrac>
+ <mi>ν</mi>
+ <mn>4</mn>
+ </mfrac>
+ <mo>−</mo>
+ <mfrac>
+ <mn>1</mn>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msub>
+ <mi>I</mi>
+ <mrow>
+ <mfrac>
+ <mi>k</mi>
+ <mn>2</mn>
+ </mfrac>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </msub>
+ <mfenced>
+ <mrow>
+ <msqrt>
+ <mrow>
+ <mi>λ</mi>
+ <mi>x</mi>
+ </mrow>
+ </msqrt>
+ </mrow>
+ </mfenced>
+ </mrow>
+</math>
+

Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref4.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref4.mml 2008-01-19 09:15:57 EST (Sat, 19 Jan 2008)
@@ -0,0 +1,182 @@
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtable>
+ <mtr>
+ <mtd>
+ <mi>P</mi>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>;</mo>
+ <mi>ν</mi>
+ <mo>,</mo>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>=</mo>
+ <mspace width="1em"/>
+ <munderover>
+ <mo>∑</mo>
+ <mrow>
+ <mi>i</mi>
+ <mo>=</mo>
+ <mn>0</mn>
+ </mrow>
+ <mi>∞</mi>
+ </munderover>
+ <msub>
+ <mi>s</mi>
+ <mi>i</mi>
+ </msub>
+ <msub>
+ <mi>t</mi>
+ <mi>i</mi>
+ </msub>
+ </mtd>
+ </mtr>
+ <mtr>
+ <mtd>
+ <msub>
+ <mi>s</mi>
+ <mn>0</mn>
+ </msub>
+ <mo>=</mo>
+ <msub>
+ <mi>u</mi>
+ <mn>0</mn>
+ </msub>
+ <mo>=</mo>
+ <msup>
+ <mi>e</mi>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <mo>,</mo>
+ <mspace width="1em"/>
+ <msub>
+ <mi>s</mi>
+ <mi>i</mi>
+ </msub>
+ <mo>=</mo>
+ <msub>
+ <mi>s</mi>
+ <mrow>
+ <mi>i</mi>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </msub>
+ <mo>+</mo>
+ <msub>
+ <mi>u</mi>
+ <mi>i</mi>
+ </msub>
+ <mo>,</mo>
+ <mspace width="1em"/>
+ <msub>
+ <mi>u</mi>
+ <mi>i</mi>
+ </msub>
+ <mo>=</mo>
+ <msub>
+ <mi>u</mi>
+ <mrow>
+ <mi>i</mi>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </msub>
+ <mfrac>
+ <mi>λ</mi>
+ <mrow>
+ <mn>2</mn>
+ <mi>i</mi>
+ </mrow>
+ </mfrac>
+ </mtd>
+ </mtr>
+ <mtr>
+ <mtd>
+ <msub>
+ <mi>t</mi>
+ <mn>0</mn>
+ </msub>
+ <mo>=</mo>
+ <mfrac>
+ <mn>1</mn>
+ <mrow>
+ <mi>Γ</mi>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </mfrac>
+ <mo>+</mo>
+ <mn>1</mn>
+ </mrow>
+ </mfenced>
+ </mrow>
+ </mfrac>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mi>x</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mrow>
+ <mfrac>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msup>
+ <mi>e</mi>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mi>x</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <mo>,</mo>
+ <mspace width="1em"/>
+ <msub>
+ <mi>t</mi>
+ <mi>i</mi>
+ </msub>
+ <mo>=</mo>
+ <msub>
+ <mi>t</mi>
+ <mrow>
+ <mi>i</mi>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </msub>
+ <mfrac>
+ <mi>x</mi>
+ <mrow>
+ <mi>ν</mi>
+ <mo>+</mo>
+ <mn>2</mn>
+ <mi>i</mi>
+ </mrow>
+ </mfrac>
+ </mtd>
+ </mtr>
+ </mtable>
+ </mrow>
+</math>
+

Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref5.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref5.mml 2008-01-19 09:15:57 EST (Sat, 19 Jan 2008)
@@ -0,0 +1,75 @@
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mi>P</mi>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>;</mo>
+ <mi>ν</mi>
+ <mo>,</mo>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>=</mo>
+ <mspace width="1em"/>
+ <munderover>
+ <mo>∑</mo>
+ <mrow>
+ <mi>i</mi>
+ <mo>=</mo>
+ <mn>0</mn>
+ </mrow>
+ <mi>∞</mi>
+ </munderover>
+ <mfrac>
+ <mrow>
+ <msup>
+ <mi>e</mi>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mi>i</mi>
+ </msup>
+ </mrow>
+ <mrow>
+ <mi>i</mi>
+ <mo>!</mo>
+ </mrow>
+ </mfrac>
+ <msub>
+ <mi>P</mi>
+ <mrow>
+ <mfrac>
+ <mi>x</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msub>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </mfrac>
+ <mo>+</mo>
+ <mi>i</mi>
+ </mrow>
+ </mfenced>
+ </mrow>
+</math>
+

Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref6.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref6.mml 2008-01-19 09:15:57 EST (Sat, 19 Jan 2008)
@@ -0,0 +1,77 @@
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mn>1</mn>
+ <mo>−</mo>
+ <mi>P</mi>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>;</mo>
+ <mi>ν</mi>
+ <mo>,</mo>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>=</mo>
+ <mspace width="1em"/>
+ <munderover>
+ <mo>∑</mo>
+ <mrow>
+ <mi>i</mi>
+ <mo>=</mo>
+ <mn>0</mn>
+ </mrow>
+ <mi>∞</mi>
+ </munderover>
+ <mfrac>
+ <mrow>
+ <msup>
+ <mi>e</mi>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mi>i</mi>
+ </msup>
+ </mrow>
+ <mrow>
+ <mi>i</mi>
+ <mo>!</mo>
+ </mrow>
+ </mfrac>
+ <msub>
+ <mi>Q</mi>
+ <mrow>
+ <mfrac>
+ <mi>x</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msub>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </mfrac>
+ <mo>+</mo>
+ <mi>i</mi>
+ </mrow>
+ </mfenced>
+ </mrow>
+</math>
+

Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref7.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_chi_squ_ref7.mml 2008-01-19 09:15:57 EST (Sat, 19 Jan 2008)
@@ -0,0 +1,86 @@
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mtable>
+ <mtr>
+ <mtd>
+ <mtext>mean</mtext>
+ </mtd>
+ <mtd>
+ <mo>=</mo>
+ </mtd>
+ <mtd>
+ <mi>ν</mi>
+ <mo>+</mo>
+ <mi>λ</mi>
+ </mtd>
+ </mtr>
+ <mtr>
+ <mtd>
+ <mtext>variance</mtext>
+ </mtd>
+ <mtd>
+ <mo>=</mo>
+ </mtd>
+ <mtd>
+ <mn>2</mn>
+ <mfenced>
+ <mrow>
+ <mi>ν</mi>
+ <mo>+</mo>
+ <mn>2</mn>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ </mtd>
+ </mtr>
+ <mtr>
+ <mtd>
+ <mtext>skewness</mtext>
+ </mtd>
+ <mtd>
+ <mo>=</mo>
+ </mtd>
+ <mtd>
+ <mfrac>
+ <mrow>
+ <msup>
+ <mn>2</mn>
+ <mrow>
+ <mfrac>
+ <mn>3</mn>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <mfenced>
+ <mrow>
+ <mi>ν</mi>
+ <mo>+</mo>
+ <mn>3</mn>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ </mrow>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mi>ν</mi>
+ <mo>+</mo>
+ <mn>2</mn>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ <mrow>
+ <mfrac>
+ <mn>3</mn>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ </mfrac>
+ </mtd>
+ </mtr>
+ </mtable>
+ </mrow>
+</math>
+

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