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<HEAD>
<TITLE>KURT function</TITLE>
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<P><font size="+3" color="green"><B>Kurtosis</B></font></P>
<P>
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<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%"><CODE>s = KURT(x)</CODE><br />
<CODE>s = KURT(w,x)</CODE></TD></TR>
</table></p>
<p>
The <code>KURT</code> function only accepts one or two vector arguments.
If only one vector is entered, the function returns the kurtosis of that vector's data. If two
vectors are entered, the first vector holds the weights and the second vector holds the data. The result is
always a scalar value.</p>
<p>
Suppose that <i>x</i> is a vector with <i>N</i> elements.</P>
<P>
A weight vector, <i>w</i>, may be entered as the first argument. The
length of <i>w</i> is assumed to also be <i>N</i>. If no weights are entered,
let <IMG WIDTH=17 HEIGHT=17 ALIGN=MIDDLE SRC="kurtI01.gif"> default to
<CODE>1</CODE>, for <IMG WIDTH=98 HEIGHT=25 ALIGN=MIDDLE SRC="kurtI02.gif">.
Define the total weight: <IMG WIDTH=108 HEIGHT=36 ALIGN=MIDDLE SRC="kurtI03.gif"></p>
<P>
The mean value, <IMG WIDTH=8 HEIGHT=11 ALIGN=BOTTOM SRC="kurtI04.gif">, is
defined by</p>
<p>
<IMG WIDTH=139 HEIGHT=36 ALIGN=MIDDLE SRC="kurtI05.gif"></p>
<P>
The kurtosis, <i>kurt</i>, is a nondimensional quantity which measures the
relative peakedness or flatness of a distribution, relative to a normal
distribution. A distribution with positive kurtosis is termed leptokurtic;
a distribution with negative kurtosis is termed platykurtic. An in-between
distribution is termed mesokurtic. The kurtosis is defined by:</P>
<P>
<IMG WIDTH=362 HEIGHT=56 ALIGN=BOTTOM SRC="kurtI06.gif"></p>
<P>
where the <i>-3</i> term makes the value zero for a normal distribution.</p>
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