scholarly journals A Gaussian model for the time development of the Sars-Cov-2 corona pandemic disease. Predictions for Germany made on March 30, 2020

2020 ◽  
Author(s):  
R. Schlickeiser ◽  
F. Schlickeiser
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Time Evolution ◽  
Central Limit ◽  
Gaussian Model ◽  
Time Development ◽  
The Central Limit Theorem ◽  
Gaussian Time ◽  
Doubling Times ◽  
Pandemic Wave

For Germany it is predicted that the first wave of the corona pandemic disease reaches its maximum of new infections on April 11th, 2020 days with 90 percent confidence. With a delay of about 7 days the maximum demand on breathing machines in hospitals occurs on April 18th, 2020 days. The first pandemic wave ends in Germany end of May 2020. The predictions are based on the assumption of a Gaussian time evolution well justified by the central limit theorem of statistics. The width and the maximum time and thus the duration of this Gaussian distribution are determined from a statistical χ2-fit to the observed doubling times before March 28, 2020.

scholarly journals A Gaussian Model for the Time Development of the Sars-Cov-2 Corona Pandemic Disease. Predictions for Germany Made on 30 March 2020

Physics ◽  
2020 ◽  
Vol 2 (2) ◽  
pp. 164-170 ◽  
Author(s):  
Reinhard Schlickeiser ◽  
Frank Schlickeiser
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Time Evolution ◽  
Central Limit ◽  
Gaussian Model ◽  
Time Development ◽  
The Central Limit Theorem ◽  
Gaussian Time ◽  
Doubling Times ◽  
Pandemic Wave

For Germany, it is predicted that the first wave of the corona pandemic disease reaches its maximum of new infections on 11 April 2020 − 3.4 + 5.4 days with 90% confidence. With a delay of about 7 days the maximum demand on breathing machines in hospitals occurs on 18 April 2020 − 3.4 + 5.4 days. The first pandemic wave ends in Germany end of May 2020. The predictions are based on the assumption of a Gaussian time evolution well justified by the central limit theorem of statistics. The width and the maximum time and thus the duration of this Gaussian distribution are determined from a statistical χ 2 -fit to the observed doubling times before 28 March 2020.

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

scholarly journals Does a central limit theorem hold for the k-skeleton of Poisson hyperplanes in hyperbolic space?

2021 ◽  
Author(s):  
Felix Herold ◽  
Daniel Hug ◽  
Christoph Thäle
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Hyperbolic Space ◽  
Central Limit ◽  
Hausdorff Measure ◽  
Rates Of Convergence ◽  
Limit Problem ◽  
Dimensional Hausdorff Measure ◽  
The Central Limit Theorem ◽  
Order Quantities

AbstractPoisson processes in the space of $$(d-1)$$ ( d - 1 ) -dimensional totally geodesic subspaces (hyperplanes) in a d-dimensional hyperbolic space of constant curvature $$-1$$ - 1 are studied. The k-dimensional Hausdorff measure of their k-skeleton is considered. Explicit formulas for first- and second-order quantities restricted to bounded observation windows are obtained. The central limit problem for the k-dimensional Hausdorff measure of the k-skeleton is approached in two different set-ups: (i) for a fixed window and growing intensities, and (ii) for fixed intensity and growing spherical windows. While in case (i) the central limit theorem is valid for all $$d\ge 2$$ d ≥ 2 , it is shown that in case (ii) the central limit theorem holds for $$d\in \{2,3\}$$ d ∈ { 2 , 3 } and fails if $$d\ge 4$$ d ≥ 4 and $$k=d-1$$ k = d - 1 or if $$d\ge 7$$ d ≥ 7 and for general k. Also rates of convergence are studied and multivariate central limit theorems are obtained. Moreover, the situation in which the intensity and the spherical window are growing simultaneously is discussed. In the background are the Malliavin–Stein method for normal approximation and the combinatorial moment structure of Poisson U-statistics as well as tools from hyperbolic integral geometry.

scholarly journals DETERMINING SOURCE CUMULANTS IN FEMTOSCOPY WITH GRAM–CHARLIER AND EDGEWORTH SERIES

2011 ◽  
Vol 26 (24) ◽  
pp. 1771-1782 ◽  
Author(s):  
H. C. EGGERS ◽  
M. B. DE KOCK ◽  
J. SCHMIEGEL
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Fourth Order ◽  
Momentum Space ◽  
Crucial Role ◽  
Gaussian Distributions ◽  
Edgeworth Series ◽  
The Central Limit Theorem ◽  
Non Gaussian

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram–Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for non-Gaussian distributions.

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