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commit f5fb4a62073d5ff5f601be78760c9a04543b21d2
Author: buildbot <[email protected]>
AuthorDate: Thu Jul 28 18:05:30 2022 +0000
Automatic Site Publish by Buildbot
---
.../Quantiles/SketchingQuantilesAndRanksTutorial.html | 17 +++++------------
1 file changed, 5 insertions(+), 12 deletions(-)
diff --git a/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
b/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
index 76fa3810..522f0502 100644
--- a/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
+++ b/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
@@ -518,9 +518,7 @@ of quantiles, ranks and their functions.</p>
<h2 id="what-is-a-rank">What is a rank?</h2>
-<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>
+<h3
id="a-rank-identifies-the-numeric-position-of-a-specific-value-in-an-enumerated-ordered-set-if-values">A
<em>rank</em> identifies the numeric position of a specific value in an
enumerated, ordered set if values.</h3>
<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>
@@ -535,13 +533,12 @@ of quantiles, ranks and their functions.</p>
<p>In our sketch library and documentation, when we refer to <em>rank</em>, we
imply <em>normalized rank</em>. However, in this tutorial, we will sometimes
use <em>natural ranks</em> to simplify the examples.</p>
<h3 id="rank-and-mass">Rank and Mass</h3>
+
<p><em>Normalized rank</em> is closely associated with the concept of
<em>mass</em>. The value associated with the rank 0.5 represents the median
value, or the center of <em>mass</em> of the entire set, where half of the
values are below the median and half are above. The concept of mass is
important to understanding the Prabability Mass Function (PMF) offered by all
the quantile sketches in the library.</p>
<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 is
associated with a particular <strong><em>rank</em></strong>.</p>
-</blockquote>
+<h3 id="a-quantile-is-a-value-that-is-associated-with-a-particular-rank">A
<em>quantile</em> is a <em>value</em> that is associated with a particular
<strong><em>rank</em></strong>.</h3>
<p><em>Quantile</em> is the general term that includes other terms that are
also quantiles.
To wit:</p>
@@ -589,13 +586,9 @@ To wit:</p>
<p>Let’s define the functions</p>
-<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>
+<h3
id="quantilerank-or-qr--return-the-quantile-value-q-associated-with-a-given-rank-r"><em>quantile(rank)</em>
or <em>q(r)</em> := return the quantile value <em>q</em> associated with a
given <em>rank, r</em>.</h3>
-<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>
+<h3
id="rankquantile-or-rq--return-the-rank-r-associated-with-the-given-quantile-q"><em>rank(quantile)</em>
or <em>r(q)</em> := return the rank <em>r</em> associated with the given
<em>quantile, q</em>.</h3>
<p>Using an example from the table:</p>
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