The StatsCircularMoments operation can be used as the WaveStats operation for circular data. You can also use the operation to perform uniformity tests or to convert periodic data of various formats to waves containing angles in radians.

Data Conversion Examples

Consider the date data in the wave dateData1 can be converted into an angle wave (in radians) using the StatsCircularMoments operation with /MODE=5. To run the operation execute the command:

StatsCircularMoments/T=1/Q /SAW/Mode=5/KUPR/RAYL dateData1
dateData1   W_AngleWave
12/25/04 20:58:45   5.06708
1/21/05 08:31:08   4.25635
1/2/05 07:53:44   0.405367
12/18/04 14:01:59   3.6483
1/28/05 01:50:50   5.67514
1/14/05 19:02:46   2.83757
1/18/05 21:32:49   3.6483
1/19/05 13:36:46   3.85098
1/8/05 00:05:24   1.62147
12/9/04 13:05:50   1.82415
12/26/04 15:18:29   5.26977
12/17/04 07:26:29   3.44562
12/4/04 00:37:08   0.810734
12/28/04 02:32:47   5.67514
1/13/05 08:02:51   2.63488
12/18/04 19:17:53   3.6483

Besides converting the date into circular data, the operation also performed the Kuiper and Rayleigh tests for uniformity. The results are stored in the wave W_CircularStats. The first part of the table represents various measures of circular statistics:

number_of_points 16
number_of_NaNs 0
C -2.7804
S -2.36277
R 3.64874
cBar -0.173775
sBar -0.147673
rBar 0.228046
tBar 3.84597
V 0.771954
v 1.71942
median 3.6483
mean_deviation 1.22877
Circular_Dispersion 8.75803
Skewness -0.0902807
Kurtosis 0.10402

The second part of the table contains the results of the Kuiper and Rayleigh tests:

Kuiper_V 1.13873
Kuiper_Critical 1.74726
Kuiper_P_Value 0.627286
Rayleigh_Z 0.832081
Rayleigh_CriticalZ 2.94819
Rayleigh_significance_prob 0.441939

Both tests indicate that H0 (uniform distribution) hypothesis can't be rejected.

Axial data

Here the input is cyclical data as shown below:

Picture0

To run the tests execute the following command:

StatsCircularMoments/mode=2/KUPR/RAYL/T=1/Q/AXD=2   axddata

The operation multiplies the data in axdData a factor of 2 (/AXD=2) and handles the input as if it contained angles in degrees (/mode=2).

The results in the "Circular Stats" table are:

number_of_points 60
number_of_NaNs 0
C 10.9331
S 9.09466
R 14.2213
cBar 0.182218
sBar 0.151578
rBar 0.237022
tBar 0.693861
V 0.762978
v 1.69682
median 0.74489
mean_deviation 1.277
Circular_Dispersion 9.08257
Skewness 0.030089
Kurtosis 0.00192745
Confidence_d 0.848389
Kuiper_V 1.58639
Kuiper_Critical 1.74726
Kuiper_P_Value 0.118182
Rayleigh_Z 3.37076
Rayleigh_CriticalZ 2.98324
Rayleigh_significance_prob 0.0336911

These results are rather interesting in that the Kuiper test does not reject uniformity while the Rayleigh test does.

Forum

Support

Gallery

Igor Pro 9

Learn More

Igor XOP Toolkit

Learn More

Igor NIDAQ Tools MX

Learn More