To understand a new method that can be used to improve upon Gaussian distribution, it is important to review the meaning and significance of a statistical term – kurtosis.
Kurtosis is a statistical term used to describe the relative distribution of data. Kurtosis is defined as the ratio of statistical moments. Normalized kurtosis is defined as the fourth statistical moment divided by the square of the second statistical moment. This is done to remove variability due to waveform amplitude from the measurement. In this normalized form, the kurtosis for Gaussian data is always 3, regardless of the RMS level or PSD. The normalized kurtosis value k can be easily computed from N samples of zero-mean waveform data, xi, using Equation 1.