Statistical laws

Statistical regularity

Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity. It is an umbrella term that covers the law of large numbers, all central limit theorems and ergodic theorems. If one throws a die once, it is difficult to predict the outcome, but if one repeats this experiment many times, one will see that the number of times each result occurs divided by the number of throws will eventually stabilize towards a specific value. Repeating a series of trials will produce similar, but not identical, results for each series: the average, the standard deviation and other distributional characteristics will be around the same for each series of trials. The notion is used in games of chance, demographic statistics, quality control of a manufacturing process, and in many other parts of our lives. Observations of this phenomenon provided the initial motivation for the concept of what is now known as frequency probability. This phenomenon should not be confused with the gambler's fallacy, because regularity only refers to the (possibly very) long run. The gambler's fallacy does not apply to statistical regularity because the latter considers the whole rather than individual cases. (Wikipedia).

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The Normal Distribution (1 of 3: Introductory definition)

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From playlist The Normal Distribution

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From playlist Regularization

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From playlist Continuous Probability Distributions in Statistics (WK 10 - QBA 237)

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From playlist Medical Statistics

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From playlist Probability Distributions

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What is a normal distribution? Properties of a normal distribution, including the empirical rule.

From playlist Probability Distributions

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In this final lecture in this short introduction to Probability and Statistics, we introduce perhaps the most important probability distibution: the normal distribution, also known as the `bell-curve'. Its role is clarified by the Central Limit theorem, a key result in Statistics, that sta

From playlist Probability and Statistics: an introduction

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This video explains how to determine normal distribution probabilities given z-scores using a free online calculator. http://dlippman.imathas.com/graphcalc/graphcalc.html

From playlist The Normal Distribution

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Non Normal Distributions

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From playlist Probability Distributions

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From playlist Kaggle Days Paris Edition | by LogicAI + Kaggle

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From playlist Turbulence: Problems at The Interface of Mathematics and Physics (Online)

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From playlist Statistical Rethinking Winter 2019

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From playlist Fundamental Problems of Quantum Physics

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NIPS 2011 Sparse Representation & Low-rank Approximation Workshop: Fast global convergence...

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From playlist NIPS 2011 Sparse Representation & Low-rank Approx Workshop

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Quantum-classical Correspondence in Chaotic PT-symmetric Systems by Eva-Maria Graefe

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From playlist Non-Hermitian Physics (ONLINE)

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Local eigenvalue statistics for random regular graphs - Bauerschmidt

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From playlist Mathematics

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From playlist Statistics (Full Length Videos)

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From playlist The Interplay between Statistics and Optimization in Learning

Related pages

Impossibility of a gambling system | Central limit theorem | Dice | Probability theory | Gambler's fallacy | Statistics | Law of large numbers