It's a Girl! Random Numbers, Simulations, and the Law of Large Numbers

2015 ◽  
Vol 20 (9) ◽  
pp. 561-564
Author(s):  
Chris Goodwin ◽  
Enrique Ortiz

Modeling using mathematics and making inferences about mathematical situations are becoming more and more prevalent in most fields of study. When we want to generalize about a population or make predictions of what could occur, we cannot use descriptive statistics. Instead, we turn to inference. Simulation and sampling are essential in building a foundation for statistical inference.

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jing Chen ◽  
Zengjing Chen

Abstract In this article, we employ the elementary inequalities arising from the sub-linearity of Choquet expectation to give a new proof for the generalized law of large numbers under Choquet expectations induced by 2-alternating capacities with mild assumptions. This generalizes the Linderberg–Feller methodology for linear probability theory to Choquet expectation framework and extends the law of large numbers under Choquet expectation from the strong independent and identically distributed (iid) assumptions to the convolutional independence combined with the strengthened first moment condition.


2006 ◽  
Vol 73 (4) ◽  
pp. 673-686 ◽  
Author(s):  
M. A. Milevsky ◽  
S. D. Promislow ◽  
V. R. Young

1995 ◽  
Vol 09 (16) ◽  
pp. 985-988 ◽  
Author(s):  
A.M. JAYANNAVAR

We have solved analytically a simple model of evolution of particles driven by identical noise. We show that the trajectories of all particles collapse into a single trajectory at long time. This synchronization also leads to violation of the law of large numbers.


1994 ◽  
Vol 72 (11) ◽  
pp. 1644-1646 ◽  
Author(s):  
Arkady S. Pikovsky ◽  
Jürgen Kurths

Bernoulli ◽  
2013 ◽  
Vol 19 (4) ◽  
pp. 1088-1121 ◽  
Author(s):  
Eugene Seneta

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