Product integral

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About the product integral

The product integral is a mathematical operator which fills the gap in the following table:

and looks like

Prodint.jpg

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 Vito Volterra in relation to the Volterra integral equations.

Installation

  1. download the LaTeX package from Richard Gill's website: http://www.math.leidenuniv.nl/~gill/prodint.tgz
  2. unpack the archive in an appropriate location of your TeX installation and run texhash to update the filename database
  3. make sure that pdftex, dvips and others can find the font mapfile prodint.map (e.g. by running updmap --enable Map=prodint.map if you have teTeX or TeXlive on Linux)
  4. place the following code before the body of your document to add the symbol to the set of mathematical symbols:
\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,serif,10pt]

\enablemathcollection[prodint]

\starttext

Your text here

\stoptext

Example

The following is the example which comes with the prodint package:

(texexec error, something is wrong with the input)

Notes

Please consider the following notes:

References and resources

C O N T E X T G A R D E N

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