Circular Moments Demo

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

dateData1W_AngleWave
12/25/04 20:58:455.06708
1/21/05 08:31:084.25635
1/2/05 07:53:440.405367
12/18/04 14:01:593.6483
1/28/05 01:50:505.67514
1/14/05 19:02:462.83757
1/18/05 21:32:493.6483
1/19/05 13:36:463.85098
1/8/05 00:05:241.62147
12/9/04 13:05:501.82415
12/26/04 15:18:295.26977
12/17/04 07:26:293.44562
12/4/04 00:37:080.810734
12/28/04 02:32:475.67514
1/13/05 08:02:512.63488
12/18/04 19:17:533.6483

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_points16
number_of_NaNs0
C-2.7804
S-2.36277
R3.64874
cBar-0.173775
sBar-0.147673
rBar0.228046
tBar3.84597
V0.771954
v1.71942
median3.6483
mean_deviation1.22877
Circular_Dispersion8.75803
Skewness-0.0902807
Kurtosis0.10402

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

Kuiper_V1.13873
Kuiper_Critical1.74726
Kuiper_P_Value0.627286
Rayleigh_Z0.832081
Rayleigh_CriticalZ2.94819
Rayleigh_significance_prob0.441939

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_points60
number_of_NaNs0
C10.9331
S9.09466
R14.2213
cBar0.182218
sBar0.151578
rBar0.237022
tBar0.693861
V0.762978
v1.69682
median0.74489
mean_deviation1.277
Circular_Dispersion9.08257
Skewness0.030089
Kurtosis0.00192745
Confidence_d0.848389
Kuiper_V1.58639
Kuiper_Critical1.74726
Kuiper_P_Value0.118182
Rayleigh_Z3.37076
Rayleigh_CriticalZ2.98324
Rayleigh_significance_prob0.0336911

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