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<A NAME="Statistics()"><!-- --></A><H3>
Statistics</H3>
<PRE>
public <B>Statistics</B>()</PRE>
<DL>
</DL>

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<B>Method Detail</B></FONT></TD>
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<A NAME="binomialStandardError(double, int)"><!-- --></A><H3>
binomialStandardError</H3>
<PRE>
public static double <B>binomialStandardError</B>(double&nbsp;p,
                                           int&nbsp;n)</PRE>
<DL>
<DD>Computes standard error for observed values of a binomial
 random variable.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>p</CODE> - the probability of success<DD><CODE>n</CODE> - the size of the sample
<DT><B>Returns:</B><DD>the standard error</DL>
</DD>
</DL>
<HR>

<A NAME="chiSquaredProbability(double, double)"><!-- --></A><H3>
chiSquaredProbability</H3>
<PRE>
public static double <B>chiSquaredProbability</B>(double&nbsp;x,
                                           double&nbsp;v)</PRE>
<DL>
<DD>Returns chi-squared probability for given value and degrees
 of freedom. (The probability that the chi-squared variate
 will be greater than x for the given degrees of freedom.)
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the value
<DT><B>Returns:</B><DD>the chi-squared probability</DL>
</DD>
</DL>
<HR>

<A NAME="FProbability(double, int, int)"><!-- --></A><H3>
FProbability</H3>
<PRE>
public static double <B>FProbability</B>(double&nbsp;F,
                                  int&nbsp;df1,
                                  int&nbsp;df2)</PRE>
<DL>
<DD>Computes probability of F-ratio.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>F</CODE> - the F-ratio<DD><CODE>df1</CODE> - the first number of degrees of freedom<DD><CODE>df2</CODE> - the second number of degrees of freedom
<DT><B>Returns:</B><DD>the probability of the F-ratio.</DL>
</DD>
</DL>
<HR>

<A NAME="normalProbability(double)"><!-- --></A><H3>
normalProbability</H3>
<PRE>
public static double <B>normalProbability</B>(double&nbsp;a)</PRE>
<DL>
<DD>Returns the area under the Normal (Gaussian) probability density
 function, integrated from minus infinity to <tt>x</tt>
 (assumes mean is zero, variance is one).
 <pre>
                            x
                             -
                   1        | |          2
  normal(x)  = ---------    |    exp( - t /2 ) dt
               sqrt(2pi)  | |
                           -
                          -inf.

             =  ( 1 + erf(z) ) / 2
             =  erfc(z) / 2
 </pre>
 where <tt>z = x/sqrt(2)</tt>.
 Computation is via the functions <tt>errorFunction</tt> and <tt>errorFunctionComplement</tt>.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>a</CODE> - the z-value
<DT><B>Returns:</B><DD>the probability of the z value according to the normal pdf</DL>
</DD>
</DL>
<HR>

<A NAME="normalInverse(double)"><!-- --></A><H3>
normalInverse</H3>
<PRE>
public static double <B>normalInverse</B>(double&nbsp;y0)</PRE>
<DL>
<DD>Returns the value, <tt>x</tt>, for which the area under the
 Normal (Gaussian) probability density function (integrated from
 minus infinity to <tt>x</tt>) is equal to the argument <tt>y</tt>
 (assumes mean is zero, variance is one).
 <p>
 For small arguments <tt>0 < y < exp(-2)</tt>, the program computes
 <tt>z = sqrt( -2.0 * log(y) )</tt>;  then the approximation is
 <tt>x = z - log(z)/z  - (1/z) P(1/z) / Q(1/z)</tt>.
 There are two rational functions P/Q, one for <tt>0 < y < exp(-32)</tt>
 and the other for <tt>y</tt> up to <tt>exp(-2)</tt>. 
 For larger arguments,
 <tt>w = y - 0.5</tt>, and  <tt>x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2))</tt>.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>y0</CODE> - the area under the normal pdf
<DT><B>Returns:</B><DD>the z-value</DL>
</DD>
</DL>
<HR>

<A NAME="lnGamma(double)"><!-- --></A><H3>
lnGamma</H3>
<PRE>
public static double <B>lnGamma</B>(double&nbsp;x)</PRE>
<DL>
<DD>Returns natural logarithm of gamma function.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the value
<DT><B>Returns:</B><DD>natural logarithm of gamma function</DL>
</DD>
</DL>
<HR>

<A NAME="incompleteBeta(double, double, double)"><!-- --></A><H3>
incompleteBeta</H3>
<PRE>
public static double <B>incompleteBeta</B>(double&nbsp;aa,
                                    double&nbsp;bb,
                                    double&nbsp;xx)</PRE>
<DL>
<DD>Returns the Incomplete Beta Function evaluated from zero to <tt>xx</tt>.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>aa</CODE> - the alpha parameter of the beta distribution.<DD><CODE>bb</CODE> - the beta parameter of the beta distribution.<DD><CODE>xx</CODE> - the integration end point.</DL>
</DD>
</DL>
<HR>

<A NAME="main(java.lang.String[])"><!-- --></A><H3>
main</H3>
<PRE>
public static void <B>main</B>(java.lang.String[]&nbsp;ops)</PRE>
<DL>
<DD>Main method for testing this class.
<P>
<DD><DL>
</DL>
</DD>
</DL>
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