文件列表:

0_REDSReview_demo.R
10_REDSs_five_distribution_Weibull_max.R
1_Asymptotic_REDSs_d_calibration.R
2_Finite_REDSs_d_calibration.R
3_Asymptotic_REDSs_RMSEcalibration.R
4_Finite_REDSs_RMSEcalibration.R
5_Asymptotic_REDSs_ismomentRMSEcalibration.R
6_Finite_REDSs_ismomentRMSEcalibration.R
7_Asymptotic_REDSs_imomentRMSEcalibration.R
8_Finite_REDSs_imomentRMSEcalibration.R
9_REDSs_five_distribution_Weibull.R
I_values.csv
Imoments_values.csv
Ismoments_values.csv
REDSReview_1.0.tar.gz
REDS_Central_Moments_Research_Report.pdf
d_values.csv
kurtPareto_91100000.csv
kurtPareto_91160.csv
kurtPareto_91180.csv
kurtPareto_91260.csv
kurtWeibull_28100000.csv
kurtWeibull_28180.csv
kurtWeibull_28260.csv
kurtWeibull_31100.csv
kurtgamma_31100.csv
kurtgamma_31100000.csv
kurtgamma_31180.csv
kurtgamma_31260.csv
kurtgnorm_21100000.csv
kurtgnorm_21180.csv
kurtgnorm_21260.csv
kurtgnorm_31100.csv
kurtlognorm_31100.csv
kurtlognorm_31100000.csv
kurtlognorm_31180.csv
kurtlognorm_31260.csv

# Robust estimations from distribution structures: Central moments. In 1954, Hodges and Lehmann demonstrated that if X and Y are independently sampled from an identical unimodal distribution, XY will exhibit symmetrical unimodality with its peak centered at zero. Building upon this foundational work, the current study delves into the structure of the kernel distribution of U -statistics. It is shown that the kth central moment kernel distributions (k > 2) derived from a unimodal distribution exhibit location invariance and is also nearly unimodal with the mode and median close to zero. This article provides an approach to study the general structure of kernel distributions. These works have been publically deposited in this Github since one year ago for a PNAS paper (I hidden some previous versions after updated new versions, https://github.com/tubanlee/NRS3333). I am introducing this work in YouTube and Quora, if you are interested, please visit: https://www.youtube.com/@Iobiomathematics or https://www.quora.com/profile/Tuobang-Li-1/answers . Also, it has been deposited in Zenodo Tuobang Li. (2022). Robust estimations for semiparametric models: Moments. https://doi.org/10.5281/zenodo.8127703 and research gate https://www.researchgate.net/publication/377974264_Robust_estimations_from_distribution_structures_II_Central_Moments Feel free to share it or contact tl@biomathematics.org, for more materials available by request. This is originally combined with REDS: Invariant Moments into a single paper, but now I think it is better to present it as a single paper.

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