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The distribution of the amplitude and phase of the mean of a sample of complex random variables

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  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

Edgeworth-type expansions are given for the distribution of (normalized versions of) the amplitude and phase of the mean of a sample of complex random variables. These expansions are transformed to polar forms with applications to modeling signals from a cell-phone. Limiting distributions of (normalized versions of) the amplitude and phase of the mean are given for the cases: (1) population mean is zero, and (2) population mean is non-zero. The results apply for distributions with finite cumulants.

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2013. "The distribution of the amplitude and phase of the mean of a sample of complex random variables," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 128-152.
    • Handle: RePEc:eee:jmvana:v:113:y:2013:i:c:p:128-152
    DOI: 10.1016/j.jmva.2012.05.017
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    References listed on IDEAS

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    1. Kortschak, Dominik & Albrecher, Hansjörg, 2010. "An asymptotic expansion for the tail of compound sums of Burr distributed random variables," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 612-620, April.
    2. Withers, C. S., 2000. "A simple expression for the multivariate Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 165-169, April.
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