2020-01-24

Ligong Chen, MD, MPH, Department of Preventive Medicine, Uniformed Services University of the Health Science

Title: "About Self-weight of Continuous Random Variable"

Considering that the normal distribution is only a special case in all unimodal distributions from left to right skewness, and the arithmetic mean will deviate from the peak of a skewed distribution curve, this presentation attempts to introduce a unified algorithm to estimate the peak of unimodal distributions. After obtaining the peak estimate of a unimodal distribution, the distribution can be treated as a combined distribution of two half-normal distributions, which have the same expectation and different variances. We can find that there is a certain mathematical relationship between a unimodal distribution and its mirror distribution, and their merged distribution must be a normal distribution, that is, under this new algorithm, normalization is a certainty. More importantly, this merged normal distribution has the same estimates of expectation and variance as its original distribution, and, considering the randomness of skewness of a sampling distribution, we can understand that this merged normal distribution has the same measurable space as its original distribution. Since the normalization doesn’t change anything, it is not necessary in data analysis. Therefore, the theoretical basis of statistics can be extended from normal distribution to unimodal distribution, while the non-parametric method will be limited to a smaller category, and may even gradually withdraw from the statistical methodological system. Since the t-test can be directly applied to skewed distributions, it is foreseeable that the methodology for genetic data analysis involving massive differential tests will be benefited greatly.

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