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Moments of the Truncated Complex Gaussian Distribution



Ryan J. Pirkl


We present arbitrary moments of the univariate and bivariate truncated complex Gaussian distribution. Using these moment expressions, we investigate the convergence of a particular infinite series of moments encountered in recent statistical analyses of scattering parameters measured in reverberation chambers. We find that the infinite series converges for particular parameterizations of the truncated distribution and may be expressed in closed form for the univariate case.
Technical Note (NIST TN) - 1560
Report Number


univariate, bivariate, circular random variables, complex Gaussian, complex normal, truncated complex Gaussian, truncated complex normal


Pirkl, R. (2011), Moments of the Truncated Complex Gaussian Distribution, Technical Note (NIST TN), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed May 26, 2024)


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Created November 1, 2011, Updated January 27, 2020