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new page to describe installation and usage of product integral symbol
= About the product integral =
The product integral is a mathematical operator which fills the gap in the following table:
<center>
<context>
\starttable[|c|c|]
\HL
\VL $\sum$ \VL $\int$ \VL \AR
\HL
\VL $\prod$ \VL ? \VL \AR
\HL
\stoptable
</context>
</center>
and looks like
<center>[[Image:Prodint.jpg]]</center>
This notation was suggested by Gill & Johansen (1990). Although the product integral is relatively unknown to most people, it performs an important role in the theory of survival analysis and Markov processes. In fact, for those people who are familiar with survival analysis, the Kaplan-Meier estimator of the survival function is the product integral of the Nelson-Aalen estimator of the cumulative intensity function. Product integration was introduced by the Italian mathematician [http://en.wikipedia.org/wiki/Vito_Volterra Vito Volterra] in relation to the Volterra integral equations.
= Installation =
# download the LaTeX package from Richard Gill's website: [http://www.math.uu.nl/people/gill/prodint.tar.gz http://www.math.uu.nl/people/gill/prodint.tar.gz]
# unpack the archive in an appropriate location of your TeX installation and run <code>texhash</code> to update the filename database
# make sure that pdftex, dvips and others can find the font mapfile prodint.map (e.g. by running <code>updmap --enable Map=prodint.map</code> if you have teTeX or TeXlive on Linux)
# place the following code before the body of your document to add the symbol to the set of mathematical symbols:
<texcode>
\definefontsynonym [MathGamma] [prodint]
\definefamilysynonym [default] [xop] [mc]
\startmathcollection [default]
\definemathsymbol [prodi] [op] [xop] [80]
\definemathsymbol [Prodi] [op] [xop] [82]
\definemathsymbol [PRODI] [op] [xop] [84]
\stopmathcollection
\loadmapfile[prodint]
\starttypescript [math] [modern,computer-modern,latin-modern,ams] [size]
\definebodyfont
[17.3pt,14.4pt,12pt,11pt,10pt,9pt,8pt,7pt,6pt,5pt,4pt] [mm] [mc=prodint]
\stoptypescript
\definetypeface [modern] [mm] [math] [modern]
[computer-modern][encoding=default]
\setupbodyfont[reset,modern,10pt]
\enablemathcollection[prodint]
\starttext
$\prodi$, $\Prodi$ and $\PRODI$
\stoptext
</texcode>
= Notes =
Please consider the following notes:
* the product integral symbol only exists in Computer Modern, therefore the code above is only valid when using this font
* this setup defines three commands: <code>\prodi</code> for inline formulae, <code>\Prodi</code> and <code>\PRODI</code> for displaystyle formulae (where the latter is slightly larger); see the sample file prodint.pdf in the archive for example usage
= References and resources =
* Gill, R.D. & Johansen, S. (1990) A survey of product-integration with a view toward application in survival analysis, ''The Annals of Statistics'', Vol. 18, pp.1501-1555.
* Richard Gill's [http://www.math.uu.nl/people/gill website] contains links to various articles articles on product integration
[[Category:Math]]
The product integral is a mathematical operator which fills the gap in the following table:
<center>
<context>
\starttable[|c|c|]
\HL
\VL $\sum$ \VL $\int$ \VL \AR
\HL
\VL $\prod$ \VL ? \VL \AR
\HL
\stoptable
</context>
</center>
and looks like
<center>[[Image:Prodint.jpg]]</center>
This notation was suggested by Gill & Johansen (1990). Although the product integral is relatively unknown to most people, it performs an important role in the theory of survival analysis and Markov processes. In fact, for those people who are familiar with survival analysis, the Kaplan-Meier estimator of the survival function is the product integral of the Nelson-Aalen estimator of the cumulative intensity function. Product integration was introduced by the Italian mathematician [http://en.wikipedia.org/wiki/Vito_Volterra Vito Volterra] in relation to the Volterra integral equations.
= Installation =
# download the LaTeX package from Richard Gill's website: [http://www.math.uu.nl/people/gill/prodint.tar.gz http://www.math.uu.nl/people/gill/prodint.tar.gz]
# unpack the archive in an appropriate location of your TeX installation and run <code>texhash</code> to update the filename database
# make sure that pdftex, dvips and others can find the font mapfile prodint.map (e.g. by running <code>updmap --enable Map=prodint.map</code> if you have teTeX or TeXlive on Linux)
# place the following code before the body of your document to add the symbol to the set of mathematical symbols:
<texcode>
\definefontsynonym [MathGamma] [prodint]
\definefamilysynonym [default] [xop] [mc]
\startmathcollection [default]
\definemathsymbol [prodi] [op] [xop] [80]
\definemathsymbol [Prodi] [op] [xop] [82]
\definemathsymbol [PRODI] [op] [xop] [84]
\stopmathcollection
\loadmapfile[prodint]
\starttypescript [math] [modern,computer-modern,latin-modern,ams] [size]
\definebodyfont
[17.3pt,14.4pt,12pt,11pt,10pt,9pt,8pt,7pt,6pt,5pt,4pt] [mm] [mc=prodint]
\stoptypescript
\definetypeface [modern] [mm] [math] [modern]
[computer-modern][encoding=default]
\setupbodyfont[reset,modern,10pt]
\enablemathcollection[prodint]
\starttext
$\prodi$, $\Prodi$ and $\PRODI$
\stoptext
</texcode>
= Notes =
Please consider the following notes:
* the product integral symbol only exists in Computer Modern, therefore the code above is only valid when using this font
* this setup defines three commands: <code>\prodi</code> for inline formulae, <code>\Prodi</code> and <code>\PRODI</code> for displaystyle formulae (where the latter is slightly larger); see the sample file prodint.pdf in the archive for example usage
= References and resources =
* Gill, R.D. & Johansen, S. (1990) A survey of product-integration with a view toward application in survival analysis, ''The Annals of Statistics'', Vol. 18, pp.1501-1555.
* Richard Gill's [http://www.math.uu.nl/people/gill website] contains links to various articles articles on product integration
[[Category:Math]]
