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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.

    2. Where the differences change sign indicates a peak.

    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: 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
        
    plot generated by sample program

Date created: 1/26/2009
Last updated: 1/26/2009
Please email comments on this WWW page to alan.heckert@nist.gov.