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commit d89fa7fdb7d887e79f21801e7f3f4d0990ce5748
Author: buildbot <[email protected]>
AuthorDate: Fri Aug 12 08:25:32 2022 +0000
Automatic Site Publish by Buildbot
---
.../SketchingQuantilesAndRanksTutorial.html | 22 +++++++++++-----------
output/docs/Tuple/TupleEngagementExample.html | 2 +-
2 files changed, 12 insertions(+), 12 deletions(-)
diff --git a/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
b/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
index e0b044e5..3d62ea39 100644
--- a/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
+++ b/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
@@ -509,16 +509,16 @@
-->
<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
+of massive data very quickly using only a small amount of space.<br />
+They allow us to compute 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
+<p>The goal of this short tutorial it to introduce the reader to some of the
basic concepts
of quantiles, ranks and their functions.</p>
<h2 id="what-is-a-rank">What is a rank?</h2>
-<h3
id="a-rank-identifies-the-numeric-position-of-a-specific-value-in-an-enumerated-ordered-set-if-values">A
<strong><em>rank</em></strong> identifies the numeric position of a specific
value in an enumerated, ordered set if values.</h3>
+<h3
id="a-rank-identifies-the-numeric-position-of-a-specific-value-in-an-enumerated-ordered-set-of-values">A
<strong><em>rank</em></strong> identifies the numeric position of a specific
value in an enumerated, ordered set of 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>
@@ -534,7 +534,7 @@ of quantiles, ranks and their functions.</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>
+<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 Probability Mass Function (PMF) offered by all
the quantile sketches in the library.</p>
<h2 id="what-is-a-quantile">What is a quantile?</h2>
@@ -546,7 +546,7 @@ To wit:</p>
<ul>
<li>A percentile is a quantile where the rank domain is divided into
hundredths. For example, “An SAT Math score of 740 is at the 95th percentile”.
The score of 740 is the quantile and .95 is the normalized rank.</li>
<li>A decile is a quantile where the rank domain is divided into tenths. For
example, “An SAT Math score of 690 is at the 9th decile (rank = 0.9).</li>
- <li>A quartile is a quantile where the rank domain is divided into forths.
For example, “An SAT Math score of 600 is at the third quartile (rank =
0.75).</li>
+ <li>A quartile is a quantile where the rank domain is divided into fourths.
For example, “An SAT Math score of 600 is at the third quartile (rank =
0.75).</li>
<li>The median is a quantile that splits the rank domain in half. For
example, “An SAT Math score of 520 is at the median (rank = 0.5).</li>
</ul>
@@ -647,7 +647,7 @@ To wit:</p>
the function <em>r(q)</em> is ambiguous. We will see how to resolve this
shortly.</p>
<h2 id="the-challenge-of-approximation">The challenge of approximation</h2>
-<p>By definiton, sketching algorithms are approximate, and they achieve their
high performance by discarding data. Suppose you feed <em>n</em> items into a
sketch that retains only <em>m < n</em> items. This means <em>n-m</em>
values were discarded. The sketch must track the value <em>n</em> used for
computing the rank and quantile functions. When the sketch reconstructs the
relationship between ranks and values <em>n-m</em> rank values are missing
creating holes in the sequence of [...]
+<p>By definition, sketching algorithms are approximate, and they achieve their
high performance by discarding data. Suppose you feed <em>n</em> items into a
sketch that retains only <em>m < n</em> items. This means <em>n-m</em>
values were discarded. The sketch must track the value <em>n</em> used for
computing the rank and quantile functions. When the sketch reconstructs the
relationship between ranks and values <em>n-m</em> rank values are missing
creating holes in the sequence o [...]
<p>The raw data might look like this, with its associated natural ranks.</p>
@@ -711,7 +711,7 @@ the function <em>r(q)</em> is ambiguous. We will see how to
resolve this shortly
<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>
+<p>How do we resolve <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>
@@ -796,21 +796,21 @@ Given <em>q</em>, search the quantile array until we find
the adjacent pair <em>
<td>Qualifying pair</td>
<td> </td>
<td> </td>
+ <td>q1</td>
+ <td>q2</td>
<td> </td>
<td> </td>
<td> </td>
- <td>q1</td>
- <td>q2</td>
<td> </td>
</tr>
<tr>
<td>Rank result</td>
<td> </td>
<td> </td>
+ <td>.357</td>
<td> </td>
<td> </td>
<td> </td>
- <td>.786</td>
<td> </td>
<td> </td>
</tr>
diff --git a/output/docs/Tuple/TupleEngagementExample.html
b/output/docs/Tuple/TupleEngagementExample.html
index c574a642..276e3fd2 100644
--- a/output/docs/Tuple/TupleEngagementExample.html
+++ b/output/docs/Tuple/TupleEngagementExample.html
@@ -518,7 +518,7 @@
<p>The X-axis is the number of days that a specific customer (identified by
some unique ID) visits our site in a 30 day period.</p>
-<p>The Y-axis is the number of distinct visitors (customers) that have visited
our site Y number of times during the 30 day period.</p>
+<p>The Y-axis is the number of distinct visitors (customers) that have visited
our site X number of times during the 30 day period.</p>
<p>Reading this histogram we can see that about 100 distinct visitors visited
our site exactly one day out of the 30 day period. About 11 visitors visited
our site on 5 different days of the 30 day period. And, it seems that we have
one customer that visited our site every day of the 30 day period! We
certainly want to encourage more of these loyal customers.</p>
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