On higher-order moment and cumulant estimation

Abstract

In this Supplementary Material, we have two sections. The first part gives the detailed derivations of the UMVUEs for the central moments, rawo moments and the cumulants when data are generated from the (negative) Binomial distribution, the Poisson distribution, the discrete/continuous uniform distribution and the exponential distribution. The second part provides extensive simulation studies to compare the performances of our proposed estimators with the maximum likelihood estimators (MLEs), the sample average estimators and the h/k-statistics.

Certifying Multilevel Coherence in the Motional State of a Trapped Ion

“…Instead, the estimator of 𝐶 and its standard deviation used in this work are derived from eq. ( 13) with additional biascorrection terms calculated from the method of moments [36] using estimators of the binomial distribution's central moments up to and including the skewness [37]. At 400 shots-per-point, any remaining bias was found by Monte-Carlo simulation to be at an order of magnitude smaller than the quoted uncertainties.…”

Traffic rate network tomography with higher‐order cumulants

“…Mixture distributions are overdispersed with variance larger than their mean, whereas for Poisson traffic flows, the mean equals the variance. Another relevant direction of research of interest lies in the development of better estimators for higher-order cumulants to reduce the number of observation samples required, see, for example, [6].…”

Method for acquiring time of flight from high aliasing signal in heat exchange fouling ultrasonic testing

“…The second order cumulant (variance) is most popular. But when the measurement noise is large, especially with colored noise or even non-additive noise, it is necessary to use higher order statistics to analyze (Chan et al, 2020; Xie et al, 2019).…”