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<div class="subTitle">edu.rit.numeric</div>
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<pre>public class <span class="strong">Mathe</span>
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extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
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<div class="block">Class Mathe provides static methods for various mathematical functions. The
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<caption><span>Methods</span><span class="tabEnd"> </span></caption>
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<tr>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<th class="colLast" scope="col">Method and Description</th>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#betai(double, double, double)">betai</a></strong>(double a,
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double b,
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double x)</code>
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<div class="block">Returns the incomplete beta function
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<I>I</I><SUB><I>x</I></SUB>(<I>a,b</I>).</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#binomProb(long, long, double)">binomProb</a></strong>(long n,
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long k,
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double p)</code>
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<div class="block">Returns the binomial probability.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#cumulBinomProb(long, long, double)">cumulBinomProb</a></strong>(long n,
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long k,
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double p)</code>
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<div class="block">Returns the cumulative binomial probability.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#erf(double)">erf</a></strong>(double x)</code>
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<div class="block">Returns the error function erf(<I>x</I>).</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#erfc(double)">erfc</a></strong>(double x)</code>
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<div class="block">Returns the complementary error function erfc(<I>x</I>).</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#gammp(double, double)">gammp</a></strong>(double a,
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double x)</code>
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<div class="block">Returns the incomplete gamma function, <I>P</I>(<I>a,x</I>).</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#gammq(double, double)">gammq</a></strong>(double a,
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double x)</code>
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<div class="block">Returns the complementary incomplete gamma function
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<I>Q</I>(<I>a,x</I>) = 1 − <I>P</I>(<I>a,x</I>).</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#log2(double)">log2</a></strong>(double x)</code>
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<div class="block">Returns the base-2 logarithm of <I>x</I>, log<SUB>2</SUB> <I>x</I>.</div>
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</td>
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</tr>
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#logBinomProb(long, long, double)">logBinomProb</a></strong>(long n,
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long k,
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double p)</code>
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<div class="block">Returns the logarithm of the binomial probability.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#logChoose(long, long)">logChoose</a></strong>(long n,
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long k)</code>
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<div class="block">Returns the natural logarithm of the binomial coefficient,
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log choose(<I>n,k</I>).</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#logFactorial(long)">logFactorial</a></strong>(long n)</code>
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<div class="block">Returns the natural logarithm of the factorial function,
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log <I>n</I>!.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#logGamma(double)">logGamma</a></strong>(double x)</code>
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<div class="block">Returns the natural logarithm of the gamma function,
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log Γ(<I>x</I>).</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#normalCDF(double, double, double)">normalCDF</a></strong>(double x,
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double mu,
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double sigma)</code>
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<div class="block">Returns the cumulative normal distribution at <TT>x</TT> for the given
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mean <TT>mu</TT> and standard deviation <TT>sigma</TT>.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Mathe.html#sqr(double)">sqr</a></strong>(double x)</code>
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<div class="block">Returns <I>x</I><SUP>2</SUP>.</div>
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<h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
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<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<h4>sqr</h4>
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<pre>public static double sqr(double x)</pre>
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<div class="block">Returns <I>x</I><SUP>2</SUP>.</div>
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<a name="log2(double)">
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<h4>log2</h4>
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<pre>public static double log2(double x)</pre>
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<div class="block">Returns the base-2 logarithm of <I>x</I>, log<SUB>2</SUB> <I>x</I>.</div>
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<a name="logGamma(double)">
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<h4>logGamma</h4>
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<pre>public static double logGamma(double x)</pre>
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<div class="block">Returns the natural logarithm of the gamma function,
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log Γ(<I>x</I>). If <I>x</I> is an integer, then
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Γ(<I>x</I>+1) = <I>x</I>!.</div>
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<h4>logFactorial</h4>
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<pre>public static double logFactorial(long n)</pre>
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<div class="block">Returns the natural logarithm of the factorial function,
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log <I>n</I>!.</div>
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</li>
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</ul>
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<a name="logChoose(long, long)">
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<h4>logChoose</h4>
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<pre>public static double logChoose(long n,
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long k)</pre>
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<div class="block">Returns the natural logarithm of the binomial coefficient,
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log choose(<I>n,k</I>).
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choose(<I>n,k</I>) = <I>n</I>!/<I>k</I>!/(<I>n</I>−<I>k</I>)!.</div>
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<h4>logBinomProb</h4>
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<pre>public static double logBinomProb(long n,
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long k,
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double p)</pre>
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<div class="block">Returns the logarithm of the binomial probability.
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<TT>logBinomProb(n,k,p)</TT> = log
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choose(<I>n,k</I>) + <I>k</I> log <I>p</I> + (<I>n</I>−<I>k</I>) log (1−<I>p</I>).</div>
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<h4>binomProb</h4>
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<pre>public static double binomProb(long n,
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long k,
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double p)</pre>
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<div class="block">Returns the binomial probability.
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<TT>binomProb(n,k,p)</TT> =
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choose(<I>n,k</I>) <I>p</I><SUP><I>k</I></SUP> (1−<I>p</I>)<SUP><I>n</I>−<I>k</I></SUP>.</div>
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<h4>cumulBinomProb</h4>
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<pre>public static double cumulBinomProb(long n,
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long k,
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double p)</pre>
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<div class="block">Returns the cumulative binomial probability. This is the sum from
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<I>i</I> = 0 to <I>k</I> of <a href="../../../edu/rit/numeric/Mathe.html#binomProb(long, long, double)"><code>binomProb(n,i,p)</code></a>.</div>
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<h4>gammp</h4>
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<pre>public static double gammp(double a,
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double x)</pre>
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<div class="block">Returns the incomplete gamma function, <I>P</I>(<I>a,x</I>).</div>
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<h4>gammq</h4>
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<pre>public static double gammq(double a,
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double x)</pre>
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<div class="block">Returns the complementary incomplete gamma function
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<I>Q</I>(<I>a,x</I>) = 1 − <I>P</I>(<I>a,x</I>).</div>
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<h4>erf</h4>
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<pre>public static double erf(double x)</pre>
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<div class="block">Returns the error function erf(<I>x</I>).</div>
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<a name="erfc(double)">
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<h4>erfc</h4>
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<pre>public static double erfc(double x)</pre>
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<div class="block">Returns the complementary error function erfc(<I>x</I>).</div>
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</li>
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<h4>normalCDF</h4>
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<pre>public static double normalCDF(double x,
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double mu,
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double sigma)</pre>
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<div class="block">Returns the cumulative normal distribution at <TT>x</TT> for the given
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mean <TT>mu</TT> and standard deviation <TT>sigma</TT>.</div>
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<a name="betai(double, double, double)">
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<h4>betai</h4>
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<pre>public static double betai(double a,
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double b,
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double x)</pre>
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<div class="block">Returns the incomplete beta function
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<I>I</I><SUB><I>x</I></SUB>(<I>a,b</I>).</div>
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