Difference between revisions of "FND-STA-Probability distribution"
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== Abstract == | == Abstract == | ||
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Probability distributions are at the core of any statistical analysis, in which modelled distributions are compared with sampled distributions to relate an observation to our theoretical understanding. This unit introduces the principles, discusses Poisson, uniform, and normal distributions, and presents methods to compare distributions with each other and quantify the difference. | Probability distributions are at the core of any statistical analysis, in which modelled distributions are compared with sampled distributions to relate an observation to our theoretical understanding. This unit introduces the principles, discusses Poisson, uniform, and normal distributions, and presents methods to compare distributions with each other and quantify the difference. | ||
<section end=abstract /> | <section end=abstract /> | ||
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== This unit ... == | == This unit ... == | ||
=== Prerequisites === | === Prerequisites === | ||
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| − | <!-- included from "ABC-unit_components. | + | <!-- included from "./data/ABC-unit_components.txt", section: "notes-external_prerequisites" --> |
You need the following preparation before beginning this unit. If you are not familiar with this material from courses you took previously, you need to prepare yourself from other information sources: | You need the following preparation before beginning this unit. If you are not familiar with this material from courses you took previously, you need to prepare yourself from other information sources: | ||
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*<b>Calculus</b>: functions and equations; polynomial functions, logarithms, trigonometric functions; integrals and derivatives; theorem and proof. | *<b>Calculus</b>: functions and equations; polynomial functions, logarithms, trigonometric functions; integrals and derivatives; theorem and proof. | ||
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You need to complete the following units before beginning this one: | You need to complete the following units before beginning this one: | ||
*[[FND-STA-Probability|FND-STA-Probability (Probability)]] | *[[FND-STA-Probability|FND-STA-Probability (Probability)]] | ||
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=== Objectives === | === Objectives === | ||
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This unit will ... | This unit will ... | ||
* ... introduce basic concepts of probability distributions; | * ... introduce basic concepts of probability distributions; | ||
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=== Outcomes === | === Outcomes === | ||
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After working through this unit you ... | After working through this unit you ... | ||
* ... can interpret observed events in terms of probability distributions; | * ... can interpret observed events in terms of probability distributions; | ||
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=== Deliverables === | === Deliverables === | ||
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*<b>Time management</b>: Before you begin, estimate how long it will take you to complete this unit. Then, record in your course journal: the number of hours you estimated, the number of hours you worked on the unit, and the amount of time that passed between start and completion of this unit. | *<b>Time management</b>: Before you begin, estimate how long it will take you to complete this unit. Then, record in your course journal: the number of hours you estimated, the number of hours you worked on the unit, and the amount of time that passed between start and completion of this unit. | ||
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*<b>Journal</b>: Document your progress in your [[FND-Journal|Course Journal]]. Some tasks may ask you to include specific items in your journal. Don't overlook these. | *<b>Journal</b>: Document your progress in your [[FND-Journal|Course Journal]]. Some tasks may ask you to include specific items in your journal. Don't overlook these. | ||
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*<b>Insights</b>: If you find something particularly noteworthy about this unit, make a note in your [[ABC-Insights|'''insights!''' page]]. | *<b>Insights</b>: If you find something particularly noteworthy about this unit, make a note in your [[ABC-Insights|'''insights!''' page]]. | ||
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<div id="BIO"> | <div id="BIO"> | ||
== Contents == | == Contents == | ||
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{{Smallvspace}} | {{Smallvspace}} | ||
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== Notes == | == Notes == | ||
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<references /> | <references /> | ||
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<div id="ABC-unit-framework"> | <div id="ABC-unit-framework"> | ||
== Self-evaluation == | == Self-evaluation == | ||
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=== Question 1=== | === Question 1=== | ||
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{{CC-BY}} | {{CC-BY}} | ||
Revision as of 01:26, 6 January 2018
Probability Distribution
Keywords: Nature of a probability distribution, important distributions, comparing observed and simulated probability distributions, Kullback-Leibler diveregence, the Kolmogorov-Smirnov test.
Contents
Abstract
Probability distributions are at the core of any statistical analysis, in which modelled distributions are compared with sampled distributions to relate an observation to our theoretical understanding. This unit introduces the principles, discusses Poisson, uniform, and normal distributions, and presents methods to compare distributions with each other and quantify the difference.
This unit ...
Prerequisites
You need the following preparation before beginning this unit. If you are not familiar with this material from courses you took previously, you need to prepare yourself from other information sources:
- Calculus: functions and equations; polynomial functions, logarithms, trigonometric functions; integrals and derivatives; theorem and proof.
You need to complete the following units before beginning this one:
Objectives
This unit will ...
- ... introduce basic concepts of probability distributions;
- ... demonstrate the Poisson, the uniform, and the normal distribution;
- ... teach how to visually and quantitatively compare them.
Outcomes
After working through this unit you ...
- ... can interpret observed events in terms of probability distributions;
- ... are familar with the Poisson, the uniform, and the normal distribution;
- ... can compare observed distributions against the normal distribution with
qqnorm(). - ... can compare observed distributions against each other with
qqplot(). - ... can use Kullback-Leibler divergence for discrete distributions, and
ks.test()for continuous distributions to quantify differences.
Deliverables
- Time management: Before you begin, estimate how long it will take you to complete this unit. Then, record in your course journal: the number of hours you estimated, the number of hours you worked on the unit, and the amount of time that passed between start and completion of this unit.
- Journal: Document your progress in your Course Journal. Some tasks may ask you to include specific items in your journal. Don't overlook these.
- Insights: If you find something particularly noteworthy about this unit, make a note in your insights! page.
Contents
Task:
- Open RStudio and load the
ABC-unitsR project. If you have loaded it before, choose File → Recent projects → ABC-Units. If you have not loaded it before, follow the instructions in the RPR-Introduction unit. - Choose Tools → Version Control → Pull Branches to fetch the most recent version of the project from its GitHub repository with all changes and bug fixes included.
- Type
init()if requested. - Open the file
FND-STA-Probability_distribution.Rand follow the instructions.
Note: take care that you understand all of the code in the script. Evaluation in this course is cumulative and you may be asked to explain any part of code.
Further reading, links and resources
Notes
Self-evaluation
If in doubt, ask! If anything about this learning unit is not clear to you, do not proceed blindly but ask for clarification. Post your question on the course mailing list: others are likely to have similar problems. Or send an email to your instructor.
About ...
Author:
- Boris Steipe <boris.steipe@utoronto.ca>
Created:
- 2017-08-05
Modified:
- 2017-08-05
Version:
- 1.0
Version history:
- 1.0 New material
This copyrighted material is licensed under a Creative Commons Attribution 4.0 International License. Follow the link to learn more.
