Difference between revisions of "Statistics notes - on random variables, distributions, probability"

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===Gaussian/Normal distribution===
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===Poisson distribution===
 
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Gaussian distribution, a.k.a. Normal distribution
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Discrete
  
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Models te probability of a given number of events occurring,
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in a fixed interval of time or space,
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based on a known mean rate,
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independently of time since last even.
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Used mainly if the events are relatively sparse; at higher rates it tends towards rh
  
Gaussian
 
* many independent identical events
 
* where things have a tendency to the average
 
* support: real numbers
 
* note: the combination of varying distributions converges on a gaussian (central point theorem), so it's a decent go-to if you don't know.
 
* The gaussian is an easy go-to in part because of the central limit theorem
 
  
 
Poisson
 
Poisson
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* useful to model likeliness of something happening in an interval -- that considers interval length, and the rarity of the events
 
* useful to model likeliness of something happening in an interval -- that considers interval length, and the rarity of the events
 
* for high rates, it starts to look more gaussian
 
* for high rates, it starts to look more gaussian
 
Note that in various cases, more than one distribution can fit the data's nature {{comment|(even when there is no real relation between the distributions. For example, for non-trivial counts both poisson and gaussian may work, which are quite different)}}.
 
 
  
  
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: Poisson -- will be mostly two and one, sometimes three, more is fairly rare. Shape is not symmatric, and we want to model the rarity.
 
: Poisson -- will be mostly two and one, sometimes three, more is fairly rare. Shape is not symmatric, and we want to model the rarity.
  
: height of body
 
*
 
  
https://en.wikipedia.org/wiki/Normal_distribution
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https://en.wikipedia.org/wiki/Poisson_distribution
 
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===Poisson distribution===
+
 
 +
===Gaussian/Normal distribution===
 
<!--
 
<!--
Discrete
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Continuous
  
https://en.wikipedia.org/wiki/Poisson_distribution
+
Gaussian distribution, a.k.a. Normal distribution
 +
 
 +
 
 +
Gaussian
 +
* many independent identical events
 +
* where things have a tendency to the average
 +
* support: real numbers
 +
* note: the combination of varying distributions converges on a gaussian (central limit theorem[https://en.wikipedia.org/wiki/Central_limit_theorem]), so it's a decent go-to if you don't know.
 +
 
 +
Note that in various cases, more than one distribution can fit the data's nature {{comment|(even when there is no real relation between the distributions. For example, for non-trivial counts both poisson and gaussian may work, which are quite different)}}.
 +
 
 +
 
 +
Examples:
 +
* height of body
 +
 
 +
 
 +
 
 +
https://en.wikipedia.org/wiki/Normal_distribution
 
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Revision as of 18:13, 4 July 2020

This is more for overview of my own than for teaching or exercise.

Overview of the areas

Arithmetic · 'elementary mathematics' and similar concepts
Set theory, Category theory
Geometry and its relatives · Topology
Elementary algebra - Linear algebra - Abstract algebra
Calculus and analysis
Logic
Semi-sorted
 : Information theory · Number theory · Decision theory, game theory · Recreational mathematics · Dynamical systems · Unsorted or hard to sort


Math on data:

  • Statistics as a field
some introduction · areas of statistics
types of data · on random variables, distributions
Virtues and shortcomings of...
on sampling · probability
glossary · references, unsorted
Footnotes on various analyses

Other data analysis, data summarization, learning

Regression · Classification, clustering, decisions · dimensionality reduction · Optimization theory, control theory
Connectionism, neural nets · Evolutionary computing



This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

Dependent versus independent

Random variables, distributions

Probability function(/distribution)

Probability mass function (discrete)

Probability density functions (continuous)

Cumulative distribution function

Expected value

A few distributions

Binomial distribution

Poisson distribution

Gaussian/Normal distribution