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 <li><a href="#getLowerBoundForBoverA(long,long,double)" tabindex="0">getLowerBoundForBoverA(long, long, double)</a></li>
 <li><a href="#getUpperBoundForBoverA(long,long,double)" tabindex="0">getUpperBoundForBoverA(long, long, double)</a></li>
 <li><a href="#getEstimateOfBoverA(long,long)" tabindex="0">getEstimateOfBoverA(long, long)</a></li>
 <li><a href="#getEstimateOfA(long,double)" tabindex="0">getEstimateOfA(long, double)</a></li>
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 <h1 title="Class BoundsOnRatiosInSampledSets" class="title">Class BoundsOnRatiosInSampledSets</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
 <div class="inheritance">org.apache.datasketches.common.BoundsOnRatiosInSampledSets</div>
 </div>
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 <div class="type-signature"><span class="modifiers">public final class </span><span class="element-name type-name-label">BoundsOnRatiosInSampledSets</span>
 <span class="extends-implements">extends <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">Object</a></span></div>
 <div class="block">This class is used to compute the bounds on the estimate of the ratio <i>|B| / |A|</i>, where:
 <ul>
 <li><i>|A|</i> is the unknown size of a set <i>A</i> of unique identifiers.</li>
 <li><i>|B|</i> is the unknown size of a subset <i>B</i> of <i>A</i>.</li>
 <li><i>a</i> = <i>|S<sub>A</sub>|</i> is the observed size of a sample of <i>A</i>
 that was obtained by Bernoulli sampling with a known inclusion probability <i>f</i>.</li>
 <li><i>b</i> = <i>|S<sub>A</sub> &cap; B|</i> is the observed size of a subset
 of <i>S<sub>A</sub></i>.</li>
 </ul></div>
 <dl class="notes">
 <dt>Author:</dt>
 <dd>Kevin Lang</dd>
 </dl>
 </div>
 </section>
 <section class="summary">
 <ul class="summary-list">
 <!-- ========== METHOD SUMMARY =========== -->
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 <div class="table-header col-first">Modifier and Type</div>
 <div class="table-header col-second">Method</div>
 <div class="table-header col-last">Description</div>
 <div class="col-first even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
 <div class="col-second even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getEstimateOfA(long,double)" class="member-name-link">getEstimateOfA</a><wbr>(long&nbsp;a,
  double&nbsp;f)</code></div>
 <div class="col-last even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
 <div class="block">Return the estimate of A.</div>
 </div>
 <div class="col-first odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
 <div class="col-second odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getEstimateOfB(long,double)" class="member-name-link">getEstimateOfB</a><wbr>(long&nbsp;b,
  double&nbsp;f)</code></div>
 <div class="col-last odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
 <div class="block">Return the estimate of B.</div>
 </div>
 <div class="col-first even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
 <div class="col-second even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getEstimateOfBoverA(long,long)" class="member-name-link">getEstimateOfBoverA</a><wbr>(long&nbsp;a,
  long&nbsp;b)</code></div>
 <div class="col-last even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
 <div class="block">Return the estimate of b over a</div>
 </div>
 <div class="col-first odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
 <div class="col-second odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getLowerBoundForBoverA(long,long,double)" class="member-name-link">getLowerBoundForBoverA</a><wbr>(long&nbsp;a,
  long&nbsp;b,
  double&nbsp;f)</code></div>
 <div class="col-last odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
 <div class="block">Return the approximate lower bound based on a 95% confidence interval</div>
 </div>
 <div class="col-first even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
 <div class="col-second even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getUpperBoundForBoverA(long,long,double)" class="member-name-link">getUpperBoundForBoverA</a><wbr>(long&nbsp;a,
  long&nbsp;b,
  double&nbsp;f)</code></div>
 <div class="col-last even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
 <div class="block">Return the approximate upper bound based on a 95% confidence interval</div>
 </div>
 </div>
 </div>
 </div>
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 <h3 id="methods-inherited-from-class-java.lang.Object">Methods inherited from class&nbsp;<a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#method-summary" title="class or interface in java.lang" class="external-link">Object</a></h3>
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 <!-- ============ METHOD DETAIL ========== -->
 <li>
 <section class="method-details" id="method-detail">
 <h2>Method Details</h2>
 <ul class="member-list">
 <li>
 <section class="detail" id="getLowerBoundForBoverA(long,long,double)">
 <h3>getLowerBoundForBoverA</h3>
 <div class="horizontal-scroll">
 <div class="member-signature"><span class="modifiers">public static</span>&nbsp;<span class="return-type">double</span>&nbsp;<span class="element-name">getLowerBoundForBoverA</span><wbr><span class="parameters">(long&nbsp;a,
  long&nbsp;b,
  double&nbsp;f)</span></div>
 <div class="block">Return the approximate lower bound based on a 95% confidence interval</div>
 <dl class="notes">
 <dt>Parameters:</dt>
 <dd><code>a</code> - See class javadoc</dd>
 <dd><code>b</code> - See class javadoc</dd>
 <dd><code>f</code> - the inclusion probability used to produce the set with size <i>a</i> and should
 generally be less than 0.5. Above this value, the results not be reliable.
 When <i>f</i> = 1.0 this returns the estimate.</dd>
 <dt>Returns:</dt>
 <dd>the approximate upper bound</dd>
 </dl>
 </div>
 </section>
 </li>
 <li>
 <section class="detail" id="getUpperBoundForBoverA(long,long,double)">
 <h3>getUpperBoundForBoverA</h3>
 <div class="horizontal-scroll">
 <div class="member-signature"><span class="modifiers">public static</span>&nbsp;<span class="return-type">double</span>&nbsp;<span class="element-name">getUpperBoundForBoverA</span><wbr><span class="parameters">(long&nbsp;a,
  long&nbsp;b,
  double&nbsp;f)</span></div>
 <div class="block">Return the approximate upper bound based on a 95% confidence interval</div>
 <dl class="notes">
 <dt>Parameters:</dt>
 <dd><code>a</code> - See class javadoc</dd>
 <dd><code>b</code> - See class javadoc</dd>
 <dd><code>f</code> - the inclusion probability used to produce the set with size <i>a</i>.</dd>
 <dt>Returns:</dt>
 <dd>the approximate lower bound</dd>
 </dl>
 </div>
 </section>
 </li>
 <li>
 <section class="detail" id="getEstimateOfBoverA(long,long)">
 <h3>getEstimateOfBoverA</h3>
 <div class="horizontal-scroll">
 <div class="member-signature"><span class="modifiers">public static</span>&nbsp;<span class="return-type">double</span>&nbsp;<span class="element-name">getEstimateOfBoverA</span><wbr><span class="parameters">(long&nbsp;a,
  long&nbsp;b)</span></div>
 <div class="block">Return the estimate of b over a</div>
 <dl class="notes">
 <dt>Parameters:</dt>
 <dd><code>a</code> - See class javadoc</dd>
 <dd><code>b</code> - See class javadoc</dd>
 <dt>Returns:</dt>
 <dd>the estimate of b over a</dd>
 </dl>
 </div>
 </section>
 </li>
 <li>
 <section class="detail" id="getEstimateOfA(long,double)">
 <h3>getEstimateOfA</h3>
 <div class="horizontal-scroll">
 <div class="member-signature"><span class="modifiers">public static</span>&nbsp;<span class="return-type">double</span>&nbsp;<span class="element-name">getEstimateOfA</span><wbr><span class="parameters">(long&nbsp;a,
  double&nbsp;f)</span></div>
 <div class="block">Return the estimate of A. See class javadoc.</div>
 <dl class="notes">
 <dt>Parameters:</dt>
 <dd><code>a</code> - See class javadoc</dd>
 <dd><code>f</code> - the inclusion probability used to produce the set with size <i>a</i>.</dd>
 <dt>Returns:</dt>
 <dd>the approximate lower bound</dd>
 </dl>
 </div>
 </section>
 </li>
 <li>
 <section class="detail" id="getEstimateOfB(long,double)">
 <h3>getEstimateOfB</h3>
 <div class="horizontal-scroll">
 <div class="member-signature"><span class="modifiers">public static</span>&nbsp;<span class="return-type">double</span>&nbsp;<span class="element-name">getEstimateOfB</span><wbr><span class="parameters">(long&nbsp;b,
  double&nbsp;f)</span></div>
 <div class="block">Return the estimate of B. See class javadoc.</div>
 <dl class="notes">
 <dt>Parameters:</dt>
 <dd><code>b</code> - See class javadoc</dd>
 <dd><code>f</code> - the inclusion probability used to produce the set with size <i>b</i>.</dd>
 <dt>Returns:</dt>
 <dd>the approximate lower bound</dd>
 </dl>
 </div>
 </section>
 </li>
 </ul>
 </section>
 </li>
 </ul>
 </section>
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	<li><a href="#getEstimateOfBoverA(long,long)" tabindex="0">getEstimateOfBoverA(long, long)</a></li>
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	<h1 title="Class BoundsOnRatiosInSampledSets" class="title">Class BoundsOnRatiosInSampledSets</h1>
	</div>
	<div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
	<div class="inheritance">org.apache.datasketches.common.BoundsOnRatiosInSampledSets</div>
	</div>
	<section class="class-description" id="class-description">
	<hr>
	<div class="horizontal-scroll">
	<div class="type-signature"><span class="modifiers">public final class </span><span class="element-name type-name-label">BoundsOnRatiosInSampledSets</span>
	<span class="extends-implements">extends <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">Object</a></span></div>
	<div class="block">This class is used to compute the bounds on the estimate of the ratio <i>\|B\| / \|A\|</i>, where:
	<ul>
	<li><i>\|A\|</i> is the unknown size of a set <i>A</i> of unique identifiers.</li>
	<li><i>\|B\|</i> is the unknown size of a subset <i>B</i> of <i>A</i>.</li>
	<li><i>a</i> = <i>\|S<sub>A</sub>\|</i> is the observed size of a sample of <i>A</i>
	that was obtained by Bernoulli sampling with a known inclusion probability <i>f</i>.</li>
	<li><i>b</i> = <i>\|S<sub>A</sub> ∩ B\|</i> is the observed size of a subset
	of <i>S<sub>A</sub></i>.</li>
	</ul></div>
	<dl class="notes">
	<dt>Author:</dt>
	<dd>Kevin Lang</dd>
	</dl>
	</div>
	</section>
	<section class="summary">
	<ul class="summary-list">
	<!-- ========== METHOD SUMMARY =========== -->
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	<h2>Method Summary</h2>
	<div id="method-summary-table">
	<div class="table-tabs" role="tablist" aria-orientation="horizontal"><button id="method-summary-table-tab0" role="tab" aria-selected="true" aria-controls="method-summary-table.tabpanel" tabindex="0" onkeydown="switchTab(event)" onclick="show('method-summary-table', 'method-summary-table', 3)" class="active-table-tab">All Methods</button><button id="method-summary-table-tab1" role="tab" aria-selected="false" aria-controls="method-summary-table.tabpanel" tabindex="-1" onkeydown="switchTab(event)" onclick="show('method-summary-table', 'method-summary-table-tab1', 3)" class="table-tab">Static Methods</button><button id="method-summary-table-tab4" role="tab" aria-selected="false" aria-controls="method-summary-table.tabpanel" tabindex="-1" onkeydown="switchTab(event)" onclick="show('method-summary-table', 'method-summary-table-tab4', 3)" class="table-tab">Concrete Methods</button></div>
	<div id="method-summary-table.tabpanel" role="tabpanel" aria-labelledby="method-summary-table-tab0">
	<div class="summary-table three-column-summary">
	<div class="table-header col-first">Modifier and Type</div>
	<div class="table-header col-second">Method</div>
	<div class="table-header col-last">Description</div>
	<div class="col-first even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
	<div class="col-second even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getEstimateOfA(long,double)" class="member-name-link">getEstimateOfA</a><wbr>(long a,
	double f)</code></div>
	<div class="col-last even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
	<div class="block">Return the estimate of A.</div>
	</div>
	<div class="col-first odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
	<div class="col-second odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getEstimateOfB(long,double)" class="member-name-link">getEstimateOfB</a><wbr>(long b,
	double f)</code></div>
	<div class="col-last odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
	<div class="block">Return the estimate of B.</div>
	</div>
	<div class="col-first even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
	<div class="col-second even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getEstimateOfBoverA(long,long)" class="member-name-link">getEstimateOfBoverA</a><wbr>(long a,
	long b)</code></div>
	<div class="col-last even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
	<div class="block">Return the estimate of b over a</div>
	</div>
	<div class="col-first odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
	<div class="col-second odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getLowerBoundForBoverA(long,long,double)" class="member-name-link">getLowerBoundForBoverA</a><wbr>(long a,
	long b,
	double f)</code></div>
	<div class="col-last odd-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
	<div class="block">Return the approximate lower bound based on a 95% confidence interval</div>
	</div>
	<div class="col-first even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code>static double</code></div>
	<div class="col-second even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4"><code><a href="#getUpperBoundForBoverA(long,long,double)" class="member-name-link">getUpperBoundForBoverA</a><wbr>(long a,
	long b,
	double f)</code></div>
	<div class="col-last even-row-color method-summary-table method-summary-table-tab1 method-summary-table-tab4">
	<div class="block">Return the approximate upper bound based on a 95% confidence interval</div>
	</div>
	</div>
	</div>
	</div>
	<div class="inherited-list">
	<h3 id="methods-inherited-from-class-java.lang.Object">Methods inherited from class <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#method-summary" title="class or interface in java.lang" class="external-link">Object</a></h3>
	<code><a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#equals(java.lang.Object)" title="class or interface in java.lang" class="external-link">equals</a>, <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#getClass()" title="class or interface in java.lang" class="external-link">getClass</a>, <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#hashCode()" title="class or interface in java.lang" class="external-link">hashCode</a>, <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#notify()" title="class or interface in java.lang" class="external-link">notify</a>, <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#notifyAll()" title="class or interface in java.lang" class="external-link">notifyAll</a>, <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#toString()" title="class or interface in java.lang" class="external-link">toString</a>, <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#wait()" title="class or interface in java.lang" class="external-link">wait</a>, <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#wait(long)" title="class or interface in java.lang" class="external-link">wait</a>, <a href="https://docs.oracle.com/en/java/javase/25/docs/api/java.base/java/lang/Object.html#wait(long,int)" title="class or interface in java.lang" class="external-link">wait</a></code></div>
	</section>
	</li>
	</ul>
	</section>
	<section class="details">
	<ul class="details-list">
	<!-- ============ METHOD DETAIL ========== -->
	<li>
	<section class="method-details" id="method-detail">
	<h2>Method Details</h2>
	<ul class="member-list">
	<li>
	<section class="detail" id="getLowerBoundForBoverA(long,long,double)">
	<h3>getLowerBoundForBoverA</h3>
	<div class="horizontal-scroll">
	<div class="member-signature"><span class="modifiers">public static</span> <span class="return-type">double</span> <span class="element-name">getLowerBoundForBoverA</span><wbr><span class="parameters">(long a,
	long b,
	double f)</span></div>
	<div class="block">Return the approximate lower bound based on a 95% confidence interval</div>
	<dl class="notes">
	<dt>Parameters:</dt>
	<dd><code>a</code> - See class javadoc</dd>
	<dd><code>b</code> - See class javadoc</dd>
	<dd><code>f</code> - the inclusion probability used to produce the set with size <i>a</i> and should
	generally be less than 0.5. Above this value, the results not be reliable.
	When <i>f</i> = 1.0 this returns the estimate.</dd>
	<dt>Returns:</dt>
	<dd>the approximate upper bound</dd>
	</dl>
	</div>
	</section>
	</li>
	<li>
	<section class="detail" id="getUpperBoundForBoverA(long,long,double)">
	<h3>getUpperBoundForBoverA</h3>
	<div class="horizontal-scroll">
	<div class="member-signature"><span class="modifiers">public static</span> <span class="return-type">double</span> <span class="element-name">getUpperBoundForBoverA</span><wbr><span class="parameters">(long a,
	long b,
	double f)</span></div>
	<div class="block">Return the approximate upper bound based on a 95% confidence interval</div>
	<dl class="notes">
	<dt>Parameters:</dt>
	<dd><code>a</code> - See class javadoc</dd>
	<dd><code>b</code> - See class javadoc</dd>
	<dd><code>f</code> - the inclusion probability used to produce the set with size <i>a</i>.</dd>
	<dt>Returns:</dt>
	<dd>the approximate lower bound</dd>
	</dl>
	</div>
	</section>
	</li>
	<li>
	<section class="detail" id="getEstimateOfBoverA(long,long)">
	<h3>getEstimateOfBoverA</h3>
	<div class="horizontal-scroll">
	<div class="member-signature"><span class="modifiers">public static</span> <span class="return-type">double</span> <span class="element-name">getEstimateOfBoverA</span><wbr><span class="parameters">(long a,
	long b)</span></div>
	<div class="block">Return the estimate of b over a</div>
	<dl class="notes">
	<dt>Parameters:</dt>
	<dd><code>a</code> - See class javadoc</dd>
	<dd><code>b</code> - See class javadoc</dd>
	<dt>Returns:</dt>
	<dd>the estimate of b over a</dd>
	</dl>
	</div>
	</section>
	</li>
	<li>
	<section class="detail" id="getEstimateOfA(long,double)">
	<h3>getEstimateOfA</h3>
	<div class="horizontal-scroll">
	<div class="member-signature"><span class="modifiers">public static</span> <span class="return-type">double</span> <span class="element-name">getEstimateOfA</span><wbr><span class="parameters">(long a,
	double f)</span></div>
	<div class="block">Return the estimate of A. See class javadoc.</div>
	<dl class="notes">
	<dt>Parameters:</dt>
	<dd><code>a</code> - See class javadoc</dd>
	<dd><code>f</code> - the inclusion probability used to produce the set with size <i>a</i>.</dd>
	<dt>Returns:</dt>
	<dd>the approximate lower bound</dd>
	</dl>
	</div>
	</section>
	</li>
	<li>
	<section class="detail" id="getEstimateOfB(long,double)">
	<h3>getEstimateOfB</h3>
	<div class="horizontal-scroll">
	<div class="member-signature"><span class="modifiers">public static</span> <span class="return-type">double</span> <span class="element-name">getEstimateOfB</span><wbr><span class="parameters">(long b,
	double f)</span></div>
	<div class="block">Return the estimate of B. See class javadoc.</div>
	<dl class="notes">
	<dt>Parameters:</dt>
	<dd><code>b</code> - See class javadoc</dd>
	<dd><code>f</code> - the inclusion probability used to produce the set with size <i>b</i>.</dd>
	<dt>Returns:</dt>
	<dd>the approximate lower bound</dd>
	</dl>
	</div>
	</section>
	</li>
	</ul>
	</section>
	</li>
	</ul>
	</section>
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