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Abstract <p>In this work, an explicit expression is obtained for the distribution function of a centered and normalized data vector containing a deterministic signal (or without a signal) and Gaussian white noise with constant variance. The obtained representation is exact and does not rely on any asymptotics for a large number of observations in particular; it is ultimately expressed through an error function and elementary functions and requires iterative calculations based on a recurrence formula.</p>

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Multivariate Distribution Function for a Centered and Normalized Time Series with Gaussian White Noise

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • R. V. Baluev,
  • V. V. Topinskiy

摘要

Abstract

In this work, an explicit expression is obtained for the distribution function of a centered and normalized data vector containing a deterministic signal (or without a signal) and Gaussian white noise with constant variance. The obtained representation is exact and does not rely on any asymptotics for a large number of observations in particular; it is ultimately expressed through an error function and elementary functions and requires iterative calculations based on a recurrence formula.