<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998) originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds * revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan * with significant contributions from: Jens Lippmann, Marek Rouchal, Martin Wilck and others --> <HTML> <HEAD> <TITLE>Distributions</TITLE> <META NAME="description" CONTENT="Distributions"> <META NAME="keywords" CONTENT="vol1"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <LINK REL="STYLESHEET" HREF="vol1.css"> <LINK REL="previous" HREF="node143.html"> <LINK REL="up" HREF="node139.html"> <LINK REL="next" HREF="node145.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html2358" HREF="node145.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html2354" HREF="node139.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html2350" HREF="node143.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html2356" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <A NAME="tex2html2357" HREF="node216.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="icons.gif/index_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html2359" HREF="node145.html">References</A> <B> Up:</B> <A NAME="tex2html2355" HREF="node139.html">Basic Functions</A> <B> Previous:</B> <A NAME="tex2html2351" HREF="node143.html">Sinc and Sinc Square</A> <BR> <BR> <!--End of Navigation Panel--> <H2><A NAME="SECTION001385000000000000000"> Distributions</A> </H2> <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{displaymath} \begin{array}{rcl} {\tt GAUSS}(x;a,b,c) &=& a \exp \left[-\ln 2 \left({2(x-b)\over c} \right)^2 \right] \\ \smallskip\\ {\tt GAUSS}(x,y;a,b,c,d,e,f) &=& a \exp \left[-\ln 2 \left({(x-b)^2 \over d^2} + {(y-c)^2 \over e^2} - {2f(x-b)(y-c) \over d\,e} \right) \right] \\ \smallskip\\ {\tt GAUSSA}(x;a,b,c) &=& {a \over {\sqrt(2\pi) c}} \exp \left[- {1\over 2} \left({(x-b)\over c} \right)^2 \right] \\ \smallskip\\ {\tt IGAUSS}(x;a,b,c) &=& a \int_{-\infty}^x \exp \left[-\ln 2 \left({2(u-b)\over c} \right)^2 \right] du\\ \smallskip\\ {\tt IGAUSSA}(x;a,b,c) &=& {a \over {\sqrt(2\pi) c}} \int_{-\infty}^x \exp \left[- {1\over 2} \left({(u-b)\over c} \right)^2 \right] du \\ \smallskip\\ {\tt CAUCHY}(x;a,b,c) &=& a {\left[ 1+\left( {2(x-b) \over c} \right)^2 \right]}^{-1} \\ \smallskip\\ {\tt LORENTZ}(x;a,b,c,d) &=& a {\left[ 1+\left( {2(x-b) \over c} \right)^2 \right]}^{-d} \\ \smallskip\\ {\tt POISSON}(x;a,b,c) &=& {a b^x \exp \left(-b\right)} \over {\Gamma \left( x + 1 \right) } \\ \smallskip\\ {\tt LAPLACE}(x;a,b,c) &=& a \exp \left[ -\ln 2 \left({2\mid x-b \mid \over c} \right) \right] \\ \smallskip\\ {\tt TRIANG}(x;a,b,c) &=& a \left( 1 - {\mid x-b \mid \over c} \right) \end{array} \end{displaymath} --> <IMG WIDTH="708" HEIGHT="745" SRC="img302.gif" ALT="\begin{displaymath}\begin{array}{rcl} {\tt GAUSS}(x;a,b,c) &=& a \exp \left[-... ...=& a \left( 1 - {\mid x-b \mid \over c} \right) \end{array}\end{displaymath}"> </DIV> <BR CLEAR="ALL"> <P></P> <P> <BR><HR> <ADDRESS> <I>Petra Nass</I> <BR><I>1999-06-09</I> </ADDRESS> </BODY> </HTML>