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Probability densities of gamma distribution

Analysis of estimation error of skewness and kurtosis of Bunimovich-Rice processes with exponentially power waveform of pulses

Aleksandr I. Krasil'nikov, Viktor S. Beregun


Mathematical expectations and variances of estimates of skewness and kurtosis coefficients of the noise signal model have been derived in this study. The specified noise signals represent the Bunimovich–Rice processes with exponentially power waveform of pulses expressed in terms of cumulant coefficients of the specified processes. It is shown that the distribution of instantaneous values of Bunimovich–Rice processes is quite different from the Gaussian distribution. The root-mean-square and relative estimation errors of skewness and kurtosis coefficients depending on of the time constant and waveform parameter of elementary pulses, as well as distributions of pulse amplitudes (degenerate and gamma distributions) and their intensities are analyzed. Expressions for finding the minimal sample volumes are obtained that ensure the specified values of relative errors in estimating the skewness and kurtosis coefficients of Bunimovich–Rice processes. The minimal sample volumes depending on parameters of these processes have been determined that ensure the relative estimation errors, which do not exceed 1%.


noise signal; Bunimovich-Rice process; skewness coefficient; kurtosis coefficient; cumulant coefficient estimate; estimation error of cumulant coefficients

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