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commit 2be9ce9e105e93563891ac32cc3a1def3d7340b5
Author: buildbot <[email protected]>
AuthorDate: Thu Jul 28 17:43:18 2022 +0000
Automatic Site Publish by Buildbot
---
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+ <li><a
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<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/HLL.html b/output/docs/HLL/HLL.html
index 73941340..25f64bde 100644
--- a/output/docs/HLL/HLL.html
+++ b/output/docs/HLL/HLL.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/HllCppExample.html
b/output/docs/HLL/HllCppExample.html
index 19705fad..83d4beba 100644
--- a/output/docs/HLL/HllCppExample.html
+++ b/output/docs/HLL/HllCppExample.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/HllHiveUDFs.html b/output/docs/HLL/HllHiveUDFs.html
index 8a15f3b4..f169e1e2 100644
--- a/output/docs/HLL/HllHiveUDFs.html
+++ b/output/docs/HLL/HllHiveUDFs.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/HllJavaExample.html
b/output/docs/HLL/HllJavaExample.html
index fa88a3a7..842d8115 100644
--- a/output/docs/HLL/HllJavaExample.html
+++ b/output/docs/HLL/HllJavaExample.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/HllMap.html b/output/docs/HLL/HllMap.html
index 18853844..a6546815 100644
--- a/output/docs/HLL/HllMap.html
+++ b/output/docs/HLL/HllMap.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/HllPerformance.html
b/output/docs/HLL/HllPerformance.html
index 6863bf47..ced73883 100644
--- a/output/docs/HLL/HllPerformance.html
+++ b/output/docs/HLL/HllPerformance.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/HllPigUDFs.html b/output/docs/HLL/HllPigUDFs.html
index 30d646ff..a03eb21c 100644
--- a/output/docs/HLL/HllPigUDFs.html
+++ b/output/docs/HLL/HllPigUDFs.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/HllSketchVsDruidHyperLogLogCollector.html
b/output/docs/HLL/HllSketchVsDruidHyperLogLogCollector.html
index 6bac9669..65dcbce0 100644
--- a/output/docs/HLL/HllSketchVsDruidHyperLogLogCollector.html
+++ b/output/docs/HLL/HllSketchVsDruidHyperLogLogCollector.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/Hll_vs_CS_Hllpp.html
b/output/docs/HLL/Hll_vs_CS_Hllpp.html
index 62ee429e..2ed01498 100644
--- a/output/docs/HLL/Hll_vs_CS_Hllpp.html
+++ b/output/docs/HLL/Hll_vs_CS_Hllpp.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/HLL/Hll_vs_G_Hllpp.html
b/output/docs/HLL/Hll_vs_G_Hllpp.html
index 732d26c3..a93355d6 100644
--- a/output/docs/HLL/Hll_vs_G_Hllpp.html
+++ b/output/docs/HLL/Hll_vs_G_Hllpp.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/KLL/KLLCppExample.html
b/output/docs/KLL/KLLCppExample.html
index e47a391c..0a3eef31 100644
--- a/output/docs/KLL/KLLCppExample.html
+++ b/output/docs/KLL/KLLCppExample.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/KLL/KLLSketch.html b/output/docs/KLL/KLLSketch.html
index 09bcc83f..cee51754 100644
--- a/output/docs/KLL/KLLSketch.html
+++ b/output/docs/KLL/KLLSketch.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Memory/MemoryComponent.html
b/output/docs/Memory/MemoryComponent.html
index 30f0a005..0b014fef 100644
--- a/output/docs/Memory/MemoryComponent.html
+++ b/output/docs/Memory/MemoryComponent.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Memory/MemoryPerformance.html
b/output/docs/Memory/MemoryPerformance.html
index deed92e7..4a28275c 100644
--- a/output/docs/Memory/MemoryPerformance.html
+++ b/output/docs/Memory/MemoryPerformance.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Quantiles/OrigQuantilesSketch.html
b/output/docs/Quantiles/OrigQuantilesSketch.html
index b02eeb78..065145f6 100644
--- a/output/docs/Quantiles/OrigQuantilesSketch.html
+++ b/output/docs/Quantiles/OrigQuantilesSketch.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Quantiles/QuantilesHiveUDFs.html
b/output/docs/Quantiles/QuantilesHiveUDFs.html
index 3969f6a4..0df93a81 100644
--- a/output/docs/Quantiles/QuantilesHiveUDFs.html
+++ b/output/docs/Quantiles/QuantilesHiveUDFs.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Quantiles/QuantilesJavaExample.html
b/output/docs/Quantiles/QuantilesJavaExample.html
index 74b0e1b9..03f43042 100644
--- a/output/docs/Quantiles/QuantilesJavaExample.html
+++ b/output/docs/Quantiles/QuantilesJavaExample.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Quantiles/QuantilesOverview.html
b/output/docs/Quantiles/QuantilesOverview.html
index 9addfce3..e1794b72 100644
--- a/output/docs/Quantiles/QuantilesOverview.html
+++ b/output/docs/Quantiles/QuantilesOverview.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Quantiles/QuantilesPigUDFs.html
b/output/docs/Quantiles/QuantilesPigUDFs.html
index 140295f1..9180fe7b 100644
--- a/output/docs/Quantiles/QuantilesPigUDFs.html
+++ b/output/docs/Quantiles/QuantilesPigUDFs.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Quantiles/QuantilesReferences.html
b/output/docs/Quantiles/QuantilesReferences.html
index f9a246fb..3fb55b1e 100644
--- a/output/docs/Quantiles/QuantilesReferences.html
+++ b/output/docs/Quantiles/QuantilesReferences.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Quantiles/QuantilesSketchOverview.html
b/output/docs/Quantiles/QuantilesSketchOverview.html
index e408d325..05f86fc1 100644
--- a/output/docs/Quantiles/QuantilesSketchOverview.html
+++ b/output/docs/Quantiles/QuantilesSketchOverview.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Quantiles/Definitions.html
b/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
similarity index 89%
rename from output/docs/Quantiles/Definitions.html
rename to output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
index 955e91f3..76fa3810 100644
--- a/output/docs/Quantiles/Definitions.html
+++ b/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
@@ -507,16 +507,22 @@
specific language governing permissions and limitations
under the License.
-->
-<h1 id="quantiles-and-ranks-definitions">Quantiles and Ranks Definitions</h1>
-<p>Streaming quantiles algorithms, or quantiles sketches, enable us to analyze
the distributions of massive data very quickly using only a small amout of
space. They allow us to compute a quantile values given a desired rank, or
compute a rank given
+<h1 id="sketching-quantiles-and-ranks-the-basics">Sketching Quantiles and
Ranks, the Basics</h1>
+<p>Streaming quantiles algorithms, or quantiles sketches, enable us to analyze
the distributions
+of massive data very quickly using only a small amout of space.<br />
+They allow us to compute a quantile values given a desired rank, or compute a
rank given
a quantile value. Quantile sketches enable us to plot the CDF, PMF or
histograms of a distribution.</p>
-<p>The goal of this short tutorial it to introduce to the reader some of the
basic concepts of quantiles, ranks and their functions.</p>
-
-<p>Before we can define <em>quantile</em>, we must first define what we mean
by <em>rank</em>.</p>
+<p>The goal of this short tutorial it to introduce to the reader some of the
basic concepts
+of quantiles, ranks and their functions.</p>
<h2 id="what-is-a-rank">What is a rank?</h2>
-<p>Given an ordered set of values the term rank can be defined two different
ways.</p>
+
+<blockquote>
+ <p>A <strong><em>rank</em></strong> identifies the numeric position of a
specific value in an enumerated ordered set if values.</p>
+</blockquote>
+
+<p>The actual enumeration can be done in several ways, but for our use here we
will define the two common ways that <em>rank</em> can be specified and that we
will use.</p>
<ul>
<li>
@@ -534,7 +540,7 @@ a quantile value. Quantile sketches enable us to plot the
CDF, PMF or histograms
<h2 id="what-is-a-quantile">What is a quantile?</h2>
<blockquote>
- <p>A <strong><em>quantile</em></strong> is a <em>value</em> that achieves a
particular <strong><em>rank</em></strong>.</p>
+ <p>A <strong><em>quantile</em></strong> is a <em>value</em> that is
associated with a particular <strong><em>rank</em></strong>.</p>
</blockquote>
<p><em>Quantile</em> is the general term that includes other terms that are
also quantiles.
@@ -583,14 +589,13 @@ To wit:</p>
<p>Let’s define the functions</p>
-<ul>
- <li>
- <p><em>quantile(rank)</em> or <em>q(r)</em> := given a <em>rank, r</em>,
return the quantile value <em>q</em> associated with the given <em>r</em>.</p>
- </li>
- <li>
- <p><em>rank(quantile)</em> or <em>r(q)</em> := given a quantile value
<em>q</em>, return the rank <em>r</em> associated with the given <em>q</em>.</p>
- </li>
-</ul>
+<blockquote>
+ <p><em>quantile(rank)</em> or <em>q(r)</em> := return the quantile value
<em>q</em> associated with a given <em>rank, r</em>.</p>
+</blockquote>
+
+<blockquote>
+ <p><em>rank(quantile)</em> or <em>r(q)</em> := return the rank <em>r</em>
associated with the given <em>quantile, q</em>.</p>
+</blockquote>
<p>Using an example from the table:</p>
@@ -711,27 +716,26 @@ the function <em>r(q)</em> is ambiguous. We will see how
to resolve this shortly
</tbody>
</table>
-<p>So how do we resove <em>q(3)</em> or <em>r(20)</em>?</p>
+<p>When the sketch deletes values it adjusts the associated ranks by
effectively increasing the “weight” of adjacent items so that they are
positionally approximately correct and the top rank corresponds to
<em>n</em>.</p>
+
+<p>How do we resove <em>q(3)</em> or <em>r(20)</em>?</p>
<h2 id="the-need-for-inequality-search">The need for inequality search</h2>
<p>The quantile sketch algorithms discussed in the literature primarily differ
by how they choose which values in the stream should be discarded. After the
elimination process, all of the quantiles sketch implementations are left with
the challenge of how to reconstruct the actual distribution, approximately and
with good accuracy.</p>
-<p>Given the presence of duplicates and absence of values from the stream we
must redefine the above quantile and rank functions as inequalities. <strong>We
also want the quantile and rank functions to retain the properties of 1:1
functions.</strong></p>
+<p>Given the presence of duplicates and absence of values from the stream we
must redefine the above quantile and rank functions as inequalities
<strong>while retaining the properties of 1:1 functions.</strong></p>
-<p>You will find examples of both of the following definitions in the research
literature. All of our library quantile sketches allow the user to choose
between the two searching criteria.</p>
+<p>One can find examples of the following definitions in the research
literature. All of our library quantile sketches allow the user to choose the
searching criteria.</p>
<p>These next examples use a small data set that mimics what could be the
result of both duplication and sketch data deletion.</p>
<h2 id="two-search-conventions-used-when-finding-ranks-rq">Two search
conventions used when finding ranks, r(q)</h2>
-<ul>
- <li>The <em>non inclusive</em> criterion for <em>r(q)</em>: (a.k.a. the
<em>LT</em> criterion)
- <ul>
- <li>Search the quantile array until we find the adjacent pair <em>{q1,
q2}</em> where <em>q1 < q <= q2</em>. Return the rank associated with
<em>q1</em>, the first of the pair.</li>
- </ul>
- </li>
-</ul>
-<p>For example <em>r(30) = 5</em></p>
+<h3 id="the-non-inclusive-criterion-for-rq-aka-the-lt-criterion">The <em>non
inclusive</em> criterion for <em>r(q)</em> (a.k.a. the <em>LT</em>
criterion):</h3>
+
+<p>Given <em>q</em>, search the quantile array until we find the adjacent pair
<em>{q1, q2}</em> where <em>q1 < q <= q2</em>. Return the rank associated
with <em>q1</em>, the first of the pair.</p>
+
+<p>For example <em>q = 30; r(30) = 5</em></p>
<table>
<thead>
@@ -762,15 +766,11 @@ the function <em>r(q)</em> is ambiguous. We will see how
to resolve this shortly
</tbody>
</table>
-<ul>
- <li>The <em>inclusive</em> criterion for <em>r(q)</em>: (a.k.a. the
<em>LE</em> criterion)
- <ul>
- <li>Search the quantile array until we find the adjacent pair <em>{q1,
q2}</em> where <em>q1 <= q < q2</em>. Return the rank associated with
<em>q1</em>, the first of the pair.</li>
- </ul>
- </li>
-</ul>
+<h3 id="the-inclusive-criterion-for-rq-aka-the-le-criterion">The
<em>inclusive</em> criterion for <em>r(q)</em> (a.k.a. the <em>LE</em>
criterion):</h3>
-<p>For example <em>r(30) = 11</em></p>
+<p>Given <em>q</em>, search the quantile array until we find the adjacent pair
<em>{q1, q2}</em> where <em>q1 <= q < q2</em>. Return the rank associated
with <em>q1</em>, the first of the pair.</p>
+
+<p>For example <em>q = 30; r(30) = 11</em></p>
<table>
<thead>
@@ -802,15 +802,12 @@ the function <em>r(q)</em> is ambiguous. We will see how
to resolve this shortly
</table>
<h2 id="two-search-conventions-when-finding-quantiles-qr">Two search
conventions when finding quantiles, q(r)</h2>
-<ul>
- <li>The <em>non inclusive</em> criterion for <em>q(r)</em> : (a.k.a. the
<em>GT</em> criterion)
- <ul>
- <li>Search the rank array until we find the adjacent pair <em>{r1,
r2}</em> where <em>r1 <= r < r2</em>. Return the quantile associated with
<em>r2</em>, the second of the pair.</li>
- </ul>
- </li>
-</ul>
-<p>For example <em>q(5) = 30</em></p>
+<h3 id="the-non-inclusive-criterion-for-qr-aka-the-gt-criterion">The <em>non
inclusive</em> criterion for <em>q(r)</em> (a.k.a. the <em>GT</em>
criterion):</h3>
+
+<p>Given <em>r</em>, search the rank array until we find the adjacent pair
<em>{r1, r2}</em> where <em>r1 <= r < r2</em>. Return the quantile
associated with <em>r2</em>, the second of the pair.</p>
+
+<p>For example <em>r = 5; q(5) = 30</em></p>
<table>
<thead>
@@ -841,13 +838,9 @@ the function <em>r(q)</em> is ambiguous. We will see how
to resolve this shortly
</tbody>
</table>
-<ul>
- <li>The <em>inclusive</em> criterion for <em>q(r)</em>: (a.k.a. the
<em>GE</em> criterion)
- <ul>
- <li>Search the rank array until we find the adjacent pair <em>{r1,
r2}</em> where <em>r1 < r <= r2</em>. Return the quantile associated with
<em>r2</em>, the second of the pair.</li>
- </ul>
- </li>
-</ul>
+<h3 id="the-inclusive-criterion-for-qr--aka-the-ge-criterion">The
<em>inclusive</em> criterion for <em>q(r)</em> (a.k.a. the <em>GE</em>
criterion):</h3>
+
+<p>Given <em>r</em>, search the rank array until we find the adjacent pair
<em>{r1, r2}</em> where <em>r1 < r <= r2</em>. Return the quantile
associated with <em>r2</em>, the second of the pair.</p>
<p>For example <em>q(11) = 30</em></p>
@@ -880,8 +873,14 @@ the function <em>r(q)</em> is ambiguous. We will see how
to resolve this shortly
</tbody>
</table>
-<p>The power of these inequality search algorithms is that the will produce
repeatable and accurate results and insensitive to duplicates and sketch
deletions.
-In addition, the way these algorithms are designed, the property of 1:1
functions are maintained.</p>
+<h2 id="these-conventions-maintain-the-11-functional-relationship">These
conventions maintain the 1:1 functional relationship</h2>
+
+<h3
id="the-non-inclusive-search-for-qr-is-the-inverse-of-the-non-inclusive-search-for-rq-therefore-q--qrq-and-r--rqr">The
non inclusive search for q(r) is the inverse of the non inclusive search for
r(q). Therefore, <em>q = q(r(q))</em> and <em>r = r(q(r))</em>.</h3>
+
+<h3
id="the-inclusive-search-for-qr-is-the-inverse-of-the-inclusive-search-for-rq-therefore-q--qrq-and-r--rqr">The
inclusive search for q(r) is the inverse of the inclusive search for r(q).
Therefore, <em>q = q(r(q))</em> and <em>r = r(q(r))</em>.</h3>
+
+<h2 id="summary">Summary</h2>
+<p>The power of these inequality search algorithms is that they produce
repeatable and accurate results, are insensitive to duplicates and sketch
deletions, and maintain the property of 1:1 functions.</p>
</div> <!-- End content -->
diff --git a/output/docs/QuantilesStudies/DruidApproxHistogramStudy.html
b/output/docs/QuantilesStudies/DruidApproxHistogramStudy.html
index 5f0679fc..0873771f 100644
--- a/output/docs/QuantilesStudies/DruidApproxHistogramStudy.html
+++ b/output/docs/QuantilesStudies/DruidApproxHistogramStudy.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/QuantilesStudies/ExactQuantiles.html
b/output/docs/QuantilesStudies/ExactQuantiles.html
index 0d95af8c..9e7461a6 100644
--- a/output/docs/QuantilesStudies/ExactQuantiles.html
+++ b/output/docs/QuantilesStudies/ExactQuantiles.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/QuantilesStudies/KllSketchVsTDigest.html
b/output/docs/QuantilesStudies/KllSketchVsTDigest.html
index fd299d0e..0cbd5264 100644
--- a/output/docs/QuantilesStudies/KllSketchVsTDigest.html
+++ b/output/docs/QuantilesStudies/KllSketchVsTDigest.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/QuantilesStudies/MomentsSketchStudy.html
b/output/docs/QuantilesStudies/MomentsSketchStudy.html
index e980c057..f59840e7 100644
--- a/output/docs/QuantilesStudies/MomentsSketchStudy.html
+++ b/output/docs/QuantilesStudies/MomentsSketchStudy.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/QuantilesStudies/QuantilesStreamAStudy.html
b/output/docs/QuantilesStudies/QuantilesStreamAStudy.html
index c9993efa..e506b092 100644
--- a/output/docs/QuantilesStudies/QuantilesStreamAStudy.html
+++ b/output/docs/QuantilesStudies/QuantilesStreamAStudy.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/REQ/ReqAccuracyAdversarial.html
b/output/docs/REQ/ReqAccuracyAdversarial.html
index 6d366769..22853c7c 100644
--- a/output/docs/REQ/ReqAccuracyAdversarial.html
+++ b/output/docs/REQ/ReqAccuracyAdversarial.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/REQ/ReqAccuracyRandomShuffledStreams.html
b/output/docs/REQ/ReqAccuracyRandomShuffledStreams.html
index eaadf5d0..90387262 100644
--- a/output/docs/REQ/ReqAccuracyRandomShuffledStreams.html
+++ b/output/docs/REQ/ReqAccuracyRandomShuffledStreams.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/REQ/ReqSketch.html b/output/docs/REQ/ReqSketch.html
index 7243dd98..5be00bc6 100644
--- a/output/docs/REQ/ReqSketch.html
+++ b/output/docs/REQ/ReqSketch.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Sampling/ReservoirSampling.html
b/output/docs/Sampling/ReservoirSampling.html
index f7f67d7b..f918b6b8 100644
--- a/output/docs/Sampling/ReservoirSampling.html
+++ b/output/docs/Sampling/ReservoirSampling.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Sampling/ReservoirSamplingJava.html
b/output/docs/Sampling/ReservoirSamplingJava.html
index 4e9d03a6..d19ac8fd 100644
--- a/output/docs/Sampling/ReservoirSamplingJava.html
+++ b/output/docs/Sampling/ReservoirSamplingJava.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Sampling/ReservoirSamplingPerformance.html
b/output/docs/Sampling/ReservoirSamplingPerformance.html
index ec9b9c8d..5facbc60 100644
--- a/output/docs/Sampling/ReservoirSamplingPerformance.html
+++ b/output/docs/Sampling/ReservoirSamplingPerformance.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Sampling/ReservoirSamplingPigUDFs.html
b/output/docs/Sampling/ReservoirSamplingPigUDFs.html
index 53472ddf..83866403 100644
--- a/output/docs/Sampling/ReservoirSamplingPigUDFs.html
+++ b/output/docs/Sampling/ReservoirSamplingPigUDFs.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Sampling/VarOptPigUDFs.html
b/output/docs/Sampling/VarOptPigUDFs.html
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--- a/output/docs/Sampling/VarOptPigUDFs.html
+++ b/output/docs/Sampling/VarOptPigUDFs.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Sampling/VarOptSampling.html
b/output/docs/Sampling/VarOptSampling.html
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--- a/output/docs/Sampling/VarOptSampling.html
+++ b/output/docs/Sampling/VarOptSampling.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/Sampling/VarOptSamplingJava.html
b/output/docs/Sampling/VarOptSamplingJava.html
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+++ b/output/docs/Sampling/VarOptSamplingJava.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
diff --git a/output/docs/SystemIntegrations/ApacheDruidIntegration.html
b/output/docs/SystemIntegrations/ApacheDruidIntegration.html
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+++ b/output/docs/SystemIntegrations/ApacheDruidIntegration.html
@@ -341,7 +341,7 @@
<a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
</p>
<div class="collapse" id="collapse_quantiles_and_histograms">
- <li><a href="/docs/Quantiles/Definitions.html">•Quantiles
Definitions</a></li>
+ <li><a
href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and
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