Sigma-z is a statistical measure of stability which is independent of
phase, frequency, and the rate of change of the frequency.
For a given time interval tau, sigma-z can measure the contribution a
pulsar or clock can make to a
time scale if there is no independent means of measuring the phase, rotational
rate, or spin-down rate.
Based upon the cubic term in a polynomial fit, it is similar to the Hadamard
Variance (normalized rms of the data third differences), but is more robust
for the case of irregularly spaced data.
The concept was first presented by Joseph H. Taylor in 1991
(Proceedings of the IEEE 79, 1054).
Matsakis, Taylor, and Eubanks (Astronomy and Astrophysics, 1997, in press)
have proposed a more rigorous and slightly revised definition.
Click here to view downloadable
fortran and unix code (version 31jul00)
which can compute sigma-z according to the newly proposed definition.
You can check your implementation of the code by using the TOA residual file
TT94-1855 (TEMPO output file which gives the MJD
followed by the TOA residual in microseconds) and comparing it to the
associated output file
(which is sigma_z computed with the fortran code using the default
options of the unix script at the end of the down-loadable code).
If you prefer, you can download all these files and more by using
anonymous ftp to access pub/sigmai_z on tycho.usno.navy.mil.