Abstract 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%.

中文翻译：

---

脉冲指数功率波形Bunimovich-Rice过程偏度和峰度估计误差分析

摘要 本研究导出了噪声信号模型偏度和峰态系数估计的数学期望和方差。指定的噪声信号代表 Bunimovich-Rice 过程，脉冲的指数功率波形以指定过程的累积系数表示。结果表明，Bunimovich-Rice 过程的瞬时值分布与高斯分布有很大不同。分析了依赖于基本脉冲的时间常数和波形参数的偏度和峰度系数的均方根和相对估计误差，以及脉冲幅度分布（退化和伽马分布）及其强度。获得用于寻找最小样本体积的表达式，以确保在估计 Bunimovich-Rice 过程的偏度和峰度系数时指定的相对误差值。已确定取决于这些过程的参数的最小样本量，以确保相对估计误差不超过 1%。