Nonparametric Statistic and the Runs Test for Stationarity - Signal Processing of Random Physiological Signals - page 70

N ( N + 1)

T −

4

Z = N ( N (8.10)

+ 1)(2 N + 1)

24

To test for ergoticity of a process, we must determine the ensemble average and
time average for each interval. The ensemble average and time average are then paired
for each interval and their differences computed. The results of an example are given in
Table 8.4.
The value from the table at T 6 , 0 . 05 is 0. Since the calculated value of 3.0 is not less
than or equal to zero (3.0 is not 0.0), the null hypothesis, H 0 , is accepted (failure to

reject H 0 ) and it is concluded that the ensemble average and time average do not differ;
thus, the process is Ergodic.
For more detailed information on nonparametric statistical procedures, see
Hollander and Wolfe [1] and Siegel [2].

<

8.3 REFERENCES

1. Hollander, M., and Wolfe, D. A. Nonparametric Statistical Methods .NewYork:John

Wiley and Sons, 1973.

2. Siegel, S. Nonparametric Statistics . New York: McGraw-Hill Book Company, 1956.

3. Au, T., Shane, R. M., and Hoel, L. A. Fundamentals of Systems Engineering: Proba-

bilistic Models . Reading, MA: Addison-Wesley Publishing Company, 1972.

4. Brown, R. G. Introduction to Random Signal Analysis and Kalman Filtering .New

York: John Wiley and Sons, 1983.

5. O'Flynn, M. Probabilities, Random Variables, and Random Processes .NewYork:

Harper & Row, Publishers, 1982.

6. Panter, P. F. Modulation, Noise, and Spectral Analysis . New York: McGraw-Hill Book

Company, 1965.