Update SketchingQuantilesAndRanksTutorial.
diff --git a/docs/Quantiles/SketchingQuantilesAndRanksTutorial.md b/docs/Quantiles/SketchingQuantilesAndRanksTutorial.md
index a3d02b5..648bb61 100644
--- a/docs/Quantiles/SketchingQuantilesAndRanksTutorial.md
+++ b/docs/Quantiles/SketchingQuantilesAndRanksTutorial.md
@@ -132,7 +132,16 @@
### The ***non inclusive*** criterion for ***r(q)*** (a.k.a. the ***LT*** criterion):
-Given *q*, search the quantile array until we find the adjacent pair *{q1, q2}* where *q1 < q <= q2*. Return the rank associated with *q1*, the first of the pair.
+<b>Definition:</b>
+Given *q*, return the rank, *r*, of the largest quantile that is strictly less than *q*.
+
+<b>Implementation:</b>
+Given *q*, search the quantile array until we find the adjacent pair *{q1, q2}* where *q1 < q <= q2*. Return the rank, *r*, associated with *q1*, the first of the pair.
+
+<b>NOTES:</b>
+
+* If the given *q* is larger than the largest quantile retained by the sketch, the sketch will return the rank of the largest retained quantile.
+* If the given *q* is smaller than the smallest quantile retained by the sketch, the sketch will return a rank of zero.
For example *q = 30; r(30) = 5*
@@ -143,7 +152,17 @@
### The ***inclusive*** criterion for ***r(q)*** (a.k.a. the ***LE*** criterion):
-Given *q*, search the quantile array until we find the adjacent pair *{q1, q2}* where *q1 <= q < q2*. Return the rank associated with *q1*, the first of the pair.
+<b>Definition:</b>
+Given *q*, return the rank, *r*, of the largest quantile that is less than or equal to *q*.
+
+<b>Implementation:</b>
+Given *q*, search the quantile array until we find the adjacent pair *{q1, q2}* where *q1 <= q < q2*. Return the rank, *r*, associated with *q1*, the first of the pair.
+
+<b>NOTES:</b>
+
+* If the given *q* is larger than the largest quantile retained by the sketch, the sketch will return the rank of the largest retained quantile.
+* If the given *q* is smaller than the smallest quantile retained by the sketch, the sketch will return a rank of zero.
+
For example *q = 30; r(30) = 11*
@@ -156,8 +175,16 @@
### The ***non inclusive*** criterion for ***q(r)*** (a.k.a. the ***GT*** criterion):
+<b>Definition:</b>
+Given *r*, return the quantile of the smallest rank that is strictly greater than *r*.
+
+<b>Implementation:</b>
Given *r*, search the rank array until we find the adjacent pair *{r1, r2}* where *r1 <= r < r2*. Return the quantile associated with *r2*, the second of the pair.
-
+
+<b>NOTES:</b>
+
+* If the given normalized rank, *r*, is equal to 1.0, there is no quantile that satisfies this criterion. This function may choose to return either a *NaN* value, or return the largest quantile retained by the sketch.
+
For example *r = 5; q(5) = 30*
| Natural Rank[]: | 1 | 3 | r1=5 | r2=7 | 9 | 11 | 13 | 14 |
@@ -166,6 +193,10 @@
### The ***inclusive*** criterion for ***q(r)*** (a.k.a. the ***GE*** criterion):
+<b>Definition:</b>
+Given *r*, return the quantile of the smallest rank that is strictly greater than or equal to *r*.
+
+<b>Implementation:</b>
Given *r*, search the rank array until we find the adjacent pair *{r1, r2}* where *r1 < r <= r2*. Return the quantile associated with *r2*, the second of the pair.
For example *q(11) = 30*
