Dataplot Vol 1 Auxiliary Chapter

# PEAKS OF FREQUENCY TABLE

Name:
PEAKS OF FREQUENCY TABLE (LET)
Type:
Let Subcommand
Purpose:
Bin (i.e., create a frequency table) a response variable and then thin the frequency table by extracting the peaks.
Description:
Binning a data variable means to divide it into classes and compute the frequency for each class. This is the numerical equivalent of a histogram.

Peaks are determined as follows:

1. Compute the difference of the frequency counts.

Also, you can specify that relative frequencies rather than counts be computed. The command

SET RELATIVE HISTOGRAM <AREA/PERCENT>

can be used to specify whether relative frequencies are computed so that the area sums to 1 or so that frequencies sum to 1. The first option, which is the default, is useful for when using the relative binning as an estimate of a probability distribution. The second option is useful when you want to see what percentage of the data falls in a given class.

Syntax 1:
LET <y2> <x2> = PEAKS OF FREQUENCY TABLE <y>
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable;
<y2> is a variable where the computed counts (or frequencies) are stored;
<x2> is a variable where the computed bin mid-points are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used for the case where the frequencies are expressed as raw counts.

Syntax 2:
LET <y2> <x2> = RELATIVE PEAKS OF FREQUENCY TABLE <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<y2> is a variable where the computed counts (or frequencies) are stored;
<x2> is a variable where the computed bin mid-points are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used for the case where the frequencies are expressed as relative frequencies.

Examples:
LET Y2 X2 = PEAKS OF FREQUENCY TABLE Y
LET Y2 X2 = PEAKS OF FREQUENCY TABLE Y SUBSET TAG > 2
LET Y2 X2 = RELATIVE PEAKS OF FREQUENCY TABLE Y
Note:
As with the histogram, you can use the CLASS WIDTH, CLASS LOWER, and CLASS UPPER commands to override these defaults.

By default, DATAPLOT uses a class width of 0.3 times the standard deviation of the variable. A number of alternative choices for class width can be set with the command

SET HISTOGRAM CLASS WIDTH

Enter HELP HISTOGRAM CLASS WIDTH for details.

Default:
None
Synonyms:
None
Related Commands:
 BINNED = Compute a frequency table. COMBINE FREQUENCY TABLE = Combine low frequency classes in a HISTOGRAM = Generate a histogram. CLASS WIDTH = Set class widths for histograms and other related commands. HISTOGRAM CLASS WIDTH = Set class widths for histograms and other related commands.
Applications:
Data Analysis
Implementation Date:
2008/4
Program:
```
let u1 = 0
let sd1 = 1
let u2 = 5
let sd2 = 3
let p = 0.6
let y = normal mixture rand numb for i = 1 1 500
.
set write decimals 4
let y2 x2 = binned y
print x2 y2
.
let y3 x3 = peaks of frequency table y
print x3 y3
.
xlimits -5 15
histogram y
.
line color blue
line dash
line thickness 0.2
let ycoor1 = 0
let npeak = size x3
.
loop for k = 1 1 npeak
let xtemp = x3(k)
let ytemp = y3(k)
drawdata xtemp ycoor1 xtemp ytemp
end of loop
```
The following output is generated.
``` VARIABLES--X2             Y2

-4.0351         1.0000
-3.0993         2.0000
-2.1636        10.0000
-1.2278        51.0000
-0.2921       112.0000
0.6437       103.0000
1.5795        41.0000
2.5152        24.0000
3.4510        27.0000
4.3868        19.0000
5.3225        29.0000
6.2583        23.0000
7.1941        22.0000
8.1298        17.0000
9.0656         7.0000
10.0014         7.0000
10.9371         3.0000
11.8729         2.0000

VARIABLES--X3             Y3

-0.2921       112.0000
3.4510        27.0000
5.3225        29.0000
```

Date created: 1/26/2009
Last updated: 1/26/2009