STAT 3743 Course Outline
LICENSE
Except where otherwise indicated, all text materials are released under the GNU Free Documentation License version 1.3.
Copyright (c) 2010 G. Jay Kerns.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".
Table of Contents
- Beginnings
- Dealing with data
- Probability
- Discrete random variables
- Continuous distributions
- Multivariate Distributions
- Sampling Distributions
- Estimation
- Hypothesis Testing
- Simple Linear Regression
- Other topics
- GNU Free Documentation License
Beginnings
What are STATISTICS?
Definition
- Experiments
- deterministic vs. random
- Sample space
- set of all possible outcomes
Examples:
- toss coin
- number of pets
- color of student's eyes
Random variables
Example
- Do a random experiment
- Make (relative) frequency table
- Make (relative) frequency histogram
Intuitive definition of probability
Probability mass functions (PMFs)
Mean, standard deviation of a random variable
Definition
Remarks
- mean is measure of center
- mean can be anything
- mean is "first moment about origin"
Example: calculate PMF, mean, variance
Mean as a measure of center
Variance as a measure of spread
Shortcut formula for variance
Empirical distribution
Mean of empirical distribution (sample mean)
Variance of the empirical distribution
Sample variance, sample standard deviation
Dealing with data
Types of data
Quantitative versus qualitative
Collect many examples of variables
-
Types of data
- quantitative
- qualitative
- logical
- missing
- other types
Quantitative data
Remarks
Examples:
-
precip -
rivers -
discoveries
Displaying quantitative data
Strip charts (dot plots)
-
overplot,stack,jitter
Histograms
- bin width issues
Stemplots
Index plots: good for data ordered in time
- methods: spikes and points
Qualitative data and factors
ID versus factors
Examples
Factors: nominal versus ordinal
Examples:
-
state.abb -
state.region
Displaying qualitative data
Contingency tables, table and prop.table
Bar graphs
-
Ex:
state.region
Pareto diagrams: like an ordered bar graph with some extra stuff
-
Ex:
state.division
Dot charts (good stuff)
-
Ex:
state.region
Other data types
- logical
- missing
Features of data distributions
Four fundamental features:
- Center
- Spread
- Shape
- Anything unusual
Symmetry versus skewness
- right and left skewed
Kurtosis
- leptokurtic, mesokurtic, platykurtic
Unusual features: clusters or gaps
-
Ex:
faithful$eruptions - granularity
-
extreme observations
- possible sources
Descriptive statistics
Measures of center
Sample mean
- advantages and disadvantages
Sample median
- advantages and disadvantages
Trimmed mean
- advantages and disadvantages
Order statistics
sort
Sample quantile, order p
First, third quartiles
Measures of spread
Sample variance: advantages and disadvantages
Meaning of s
- Chebychev's Rule
- Empirical Rule
Interquartile range (IQR)
- advantages and disadvantages
Median Absolute Deviation
- advantages and disadvantages
Range: disadvantages
Measures of shape
Sample skewness
- Remarks
- Rule of thumb
Sample excess kurtosis
- Remarks
- Rule of thumb
Why is it "-3"?
How to do it with R
library(e1071), skewness, kurtosis
University closed (Labor Day).
Measure of spread: range
Advantages and disadvantages
Ex: stack.loss
Sample skewness
-
Ex:
stack.loss -
Ex:
discoveries(check rule of thumb)
Sample excess kurtosis
-
Ex:
stack.loss -
Ex:
UKDriverDeaths(check rule of thumb)
Exploratory data analysis
More on stemplots
- trim outliers
- split stems
- depths
Ex: faithful$eruptions
Hinges and the Five number summary
Upper, lower hinges
5NS
fivenum
Boxplots
Visual display of the 5NS
Can judge CUSS
Outliers
Potential versus suspected
Rules of thumb for both
Ex: rivers
Standardizing variables
Measure of relative standing: z-score
scale
Ex: precip
Bi/Multivariate data
Data frames: rectangular arrays of data
- same number of rows each column
- data in each column must be same type
- indexing: two dimensional
Access columns of data frames in multiple ways
Qualitative versus qualitative
Descriptive statistics: two-way tables
xtabs
addmargins
colPercents, rowPercents
Plotting two categorical variables
- Stacked bar charts
- Side-by-side bar charts
- Spine plots
Ex: Titanic data
Quantitative versus quantitative
Plotting two quantitative variables
Univariate displays separately
Association:
- linear versus nonlinear
- strong versus weak
Ex: Puromycin data
Ex: attenu data
Ex: faithful data
Ex: iris data
Measuring linear association
Sample Pearson product-moment correlation coefficient (r)
Properties of r
Ex: iris data
Ex: attenu data
More about r
- measures strength and direction of linear association
- rules of thumb
- r approx 0 doesn't mean no association
One quantitative, one qualitative
Comparison of groups
Ex: weight ~ feed, data = chickwts
Ex: ~ age | education, data = infert
Ex: ~ count | spray, data = InsectSprays
Multiple variables
Multi-way contingency tables
Mosaic plots, dot charts
Sample variance-covariance matrices
Scatterplot matrices (SPLOM)
Comparing groups: coplots
Ex: LifeCycleSavings data
Ex: Titanic data
Probability
Fundamental notions
Random experiment
Sample space
Subsets, events, empty set
Set theory review
Operations:
- union
- intersection
- difference
- complement
Algebra of sets
- identities
- commutative, associative, distributive
Examples: events in plain English, write set notation
Mutually exclusive, disjoint
Probability as limiting relative frequency
Axioms for Probability
- P(A) nonnegative
- P(S) = 1
- Probability of disjoint union is sum of probabilities
Properties of probability
- complement
- probability of null event
- monotone
- P(A) between zero and one
- General addition rule (for many events)
- Boole's inequality
Probability assignment: equally likely model
P(A) = #(A)/#(S)
Examples: tossing coins, etc.
How to count
Multiplication principle
Examples
Selecting ordered samples
- examples
Selecting unordered samples
More about binomial coefficients, Pascal's triangle
Birthday problem
Poker hands
- royal flush
- four of a kind
Conditional probability
Example: draw 2 cards, without replacement
Definition
Example: toss a coin twice
Example: toss a die twice
- A = {outcomes match}
- B = {sum of outcomes >= 8}
Properties
- P(B|A) nonnegative
- P(S|A) = 1
- cond. prob of disjoint union is sum of cond. probs
More properties
- Multiplication rule
- P(A and B) = P(A)*P(B|A)
Mult. rule for several events
Examples
Good example: transferred ball
Independence
Example: toss two coins
Definition, intuition
Proposition: A, B independent then so are complements
Mutual Independence
Example: toss 100 coins
Pairwise doesn't imply mutual
Example: computers in series
Bayes' Rule
The theorem
Picture
What does it mean?
What does [Bayes' Rule] mean?
Example: misfiling assistants
Random variables
Definition
Support set
Examples
- toss coin n times
- toss coin until heads
- toss coin, wait until lands
Discrete random variables
Tools of the trade
Definition
Probability mass functions (PMFs)
Every PMF satisfies…
Example: toss coin four times, X = #Heads
- set up function, find PMF, draw graph
Mean, variance, standard deviation
- calculate mean for previous example
Remarks
- μ can be any number
- μ is measure of center
- interpretation
Cumulative distribution functions (CDFs)
Definition
Properties
- nondecreasing
- right-continuous
- limits at infinity
Example: toss coin 3 times
- find CDF
Discrete uniform distribution
Definition, PMF, notation
Examples
Find mean and variance of =disunif=(m)
Example: find mean/variance for rolling die
Bernoulli/Binomial model
Bernoulli model
Mean and variance
Binomial model
- n Bernoulli trials
- trials independent
- prob p doesn't change
Definition, PMF, notation
Check sum of f(x) is 1
Binomial series
Find mean, variance of =binom=(n,p)
Example: five child family
How to do it with R
Example: roll 15 dice
Find/plot binomial CDFs
Connection to distr*** family of packages
Expectation
Definition
Examples: mean/variance
Properties
- E(c)=c
- E(cX) = cE(X)
- E[g(X)+h(X)] = Eg(X) + Eh(X)
Ex: discrete uniform
Ex: binomial mean (from definition)
Moment generating functions (MGF)
Definition
M(0) = 1
Ex: discrete uniform MGF
Ex: binomial MGF
- Why do they call it a MGF?
M'(0) = E(X) etc.
Ex: binomial mean
Ex: binomial variance
- Applications
Uniqueness theorem
Ex: binomial MGF
- Another connection
Taylor series of f about a
Empirical distribution
Definition
- mean
- variance
- CDF
Hypergeometric distribution
Dependent Bernoulli trials
Example
PMF, mean, variance
Example
Example of R functions for discrete probabilities
-
dbinom -
pbinom -
pbinom,lower.tail = FALSE -
distrExpackage,E(X),var(X) - plots
Waiting time distributions
Geometric distribution
PMF, mean, variance, MGF
Ex: Jeff Reed
Negative Binomial distribution
PMF, mean, variance, MGF
Poisson distribution
PMF, mean, variance, MGF
Continuous distributions
Tools of the trade
Continuous random variables
Definition
Probability density functions (PDF)
Properties
- nonnegative
- integral is one
- probability is area under the curve
- remarks
Continuous CDFs
- nondecreasing
- continuous function
- limits at infinity
- derivative of CDF is PDF
Expectation
- mean, variance, MGF
Examples
-
finite support:
beta(4,1)- integral 1, probability, μ, σ
-
infinite support:
exp(rate = 5)- integral 1, prob, μ, σ
Continuous uniform distribution
PDF, CDF, notation, R code, MGF
Find the mean, variance
Special case: unif(min = 0, max = 1)
Normal distribution
PDF, notation, R code
Standard normal: Z
φ, Φ
If X ~ norm(m,s) then Z = (X-m)/s ~ norm(0,1)
MGF of Z
MGF of X
MGF of Y = a + bX
68-95-99.7 (Empirical) Rule
Example: find P(a < X < b) for something, say, IQ
Quantiles and the quantile function
Want to go in reverse: given area, find the IQ
Quantile functions
Definition of quantile function:
Q(p) = min{x : F(x) >= p}, 0 < p < 1
Properties:
- defined, finite for 0 < p < 1
- left continuous
- reflect F about line y=x (continuous case)
- boundary limits exist but may be infinite
Special case: normal distribution
Define zα
Examples
z0.025, z0.01, z0.005
Functions of random variables
The idea
Discrete case
Make a table, accumulate probabilities
Example: X ~ binom, Y = something
PDF method
Introduce the formula and conditions
Intuitive formula
Example: X ~ norm, Y = linear transformation
Fact: if X is any norm then lin. trans. is also normal
Example: X ~ norm, Y = exp(X) (lognormal)
CDF method
Introduce the method
Example: X ~ unif(0,1), Y = -ln(X) (exponential)
Probability Integral Transform
Why the PIT is important
Probability Integral Transform
How to do it with R
Other distributions
Exponential distribution
PDF, Graph, Notation, CDF, Graph
Find the MGF
Find the mean, variance
Memoryless property
Relationship with Poisson model
Gamma distribution
PDF, Notation, Parameters
The Gamma Function
Properties of the Gamma Function
MGF, mean and variance
Motivation: relationship with Poisson process
Example: car wash
How to do it with R
Special case: Chi square distribution
Even more continuous distributions
- Cauchy
- Beta
- Logistic
- Lognormal
- Weibull
- Student's t distribution
- F distribution
Multivariate Distributions
Comparison of univariate versus multivariate
Discrete case: joint PMFs, CDFs
Example: roll fair die twice
Joint distributions
Example: roll fair die twice
Marginal distributions
Continuous case: joint PDFs, marginals
Joint expectation
Definition
Independence
Analogy with independent events
Definition (pairwise)
Comment for multivariate mutual independence
Independent, Identically Distributed (IID)
Simple Random Sample of size n
Expectation of functions of independent random variables
Sampling Distributions
Simple Random Samples
BACKGROUND
Mean and variance of linear combination of independent sample
Mean and variance of X-bar
MGF of linear combination of independent sample
MGF of X-bar
Example: SRS(11) from gamma, find dist'n of X-bar
Proposition: SRS(n) from norm, then X-bar is normal, too
Sum of independent chisq is chisq, and df's add
Sum of squared standard normals is chisq with df = n
Theorem: SRS(n) from norm, then
- X-bar and S2 are independent
-
S2 is scaled
chisqwithdf= n - 1
Linear combinations of independent normals is normal, too
Central Limit Theorem
statement of the theorem
Remarks:
- if X's are normal, then X-bar is normal
- if X's are close to normal, then X-bar is close to normal, too
- Discrete/continuous doesn't matter
- how large is large?
Example: SRS(40) have μ = 21 and σ = 7. Find probability for X-bar.
Student's t distribution and the F distribution
Student's t
where it comes from, notation
Remarks
-
looks like
normbut with heavy tails -
as
dfgets large approachesnorm(0,1)
Why it's called "Student's t" and William Sealy Gosset
F distribution
where it comes from, notation
Sir Ronald Aylmer Fisher and Snedecor
Graphs of the PDF
If F ~ f(n1,n2) then 1/F ~ f(n2,n1)
Other types of sampling distributions
Two norm samples, difference in means
Simulation based
Estimation
Maximum likelihood
Example: go fishing, count the number of sharks
Likelihood function, L
Maximize L, for us, with derivative
X-bar pops out of nowhere!
Check it's a max with FDT or SDT
General case for maximum likelihood
Remarks
- MLE: maximum likelihood estimator
- point estimators of a parameter
- sometimes take logs before differentiating
Example: MLE for geom distribution
More remarks
- can do it for more than one parameter
- sometimes need sophisticated numerical methods
- MLEs not unique, in general
- sometimes an MLE does not exist
- MLEs are just one of many types of point estimator
Definition of unbiased estimator
Example: X-bar is unbiased in the sharks problem
Example: in two-parameter norm case, MLE of variance is biased, but sample variance is unbiased
Confidence intervals for means
why CI's are important for estimation
intuition for the z-interval
Definition of z-interval, confidence interval, confidence coefficient
Example: 90% confidence interval for μ
Remarks
- for fixed confidence, as sample size increases the CI gets shorter
- for fixed sample size, as confidence increases the CI gets wider
Example: SRS(10) from pop'n, find 95% CI for μ
- identify Parameter of interest, in context
- check Assumptions
- choose relevant Name of procedure based on above
- actually calculate the Interval
- state Conclusion, in context of problem
PANIC
If σ is unknown, use s instead
Remarks
- if n is large then approx 100(1 - α )% confidence
- if n small
– if pop'n normal then use Student's t critical value, get t-interval – if pop'n non-normal — if approx normal then still not too bad — if highly skewed or outliers, ask statistician
- can have one-sided intervals, too
Example: SRS(7) from pop'n, assume norm, find CI for μ
Confidence intervals for difference of two means
intuition for the confidence interval
First suppose variances known: two-sample z-interval
If variances are unknown:
- samples both large: use sample variances, approximate 100(1-α )% confidence
- one (or both) samples small, then in trouble unless
– pop'ns both normal — if variances equal: pooled t-interval — variances unequal: Welch interval
Example: independent SRS(4) and SRS(7), norm
Welch-Aspin interval explained
How to do it with R
Confidence intervals for proportions
Examples of proportions
The asymptotic z-interval for proportions
Example: SRS(4791) from binom, find 95% CI for p
Score interval: see book
Confidence intervals (asymptotic) for two proportions
One-sided CIs for p
How to do it with R
Sample size
margin of error, E
sample sizes for means, easy
Example: find n such that x-bar plus/minus E is 95% CI
Remarks
- always round up
For proportions, little bit harder
- replace p with prior guess
- replace p(1 - p) with 1/4, can't do worse
Example: monkeys who don't like bananas, find sample size for proportion, both methods
Sample size for small pop'ns, use hypergeometric distribution
Hypothesis Testing
For proportions
Example: shotgun machine, want to improve performance, install thing-a-majig
Terminology
- null hypothesis
- alternative hypothesis
Basic hypothesis testing procedure
- set up hypotheses, collect some data
- assume null is true, construct 95% CI for parameter
- if CI doesn't cover null value, reject H0, otherwise, don't reject
More terminology
- Type I error, Type II error
- significance level
- rejection region
- two-sided and one-sided tests
Tests of hypotheses for one proportion (asymptotic)
Draw pictures
Example: observe bunch of shotguns, do hypothesis test
Example: do another hypothesis test, but for different significance levels
p-value of a hypothesis test
Example: find p-value for previous test
Hypothesis testing: "reject H0 if p-value is small"
Tests of hypotheses for two proportions
For one mean and/or one variance
Given SRS(n) from norm, unknown mean
For means
- σ known: z-tests for one mean
- σ unknown: t-tests for one mean
If σ unknown but n is large then use z-test
Example: SRS(9) from norm, hypothesis test for the mean, find p-value
More about p-values
Standard error of the sample mean
Standard errors in general
For variances
Tests of hypothesis for a variance
Example: salary from RcmdrTestDrive
How to do it with R
sigma.test from the TeachingDemos package
For two means and/or two variances
For two means
Independent two-sample t-test (pooled)
Example: mean before by smoking in RcmdrTestDrive
Remarks
- two-sample z-test
- large sample approximation
For two variances
Two-sample F-test
Example: variance of before by smoking in RcmdrTestDrive
How to do it with R
var.test from base R
Remarks
- side-by-side displays
- watch assumptions
– normality – equal variances
For paired samples
Paired t-test
Example: compare before vs. after in RcmdrTestDrive
Simple Linear Regression
Motivation
Regression Assumptions
What does it mean?
Maximum likelihood derivation of least-squares
Parameter estimates
Example: salary modeled by order in RcmdrTestDrive
How to do it with R: the lm function
Take a look at the fitted line
Residuals = ACTUAL - PREDICTED
MLE of residual standard error
Why is it called "Regression"?
Interval estimation
Sampling distributions
Confidence intervals for regression parameters
How to do it with R
Residual analysis
Graphically/numerically
Assess normality
Assess constant variance
Assess independence
Other topics
Chi-square goodness of fit
Karl Pearson (1900)
Motivation/derivation
Remarks
- observed versus expected
- rule of thumb: expected counts at least 5
Example: Gregor Mendel's corn
How to do it with R
Analysis of Variance (ANOVA)
Motivation
ANOVA Decomposition
Between vs. within
Sampling dist's of SSTO, SSE
Cochran's Theorem
Sampling dist'n of SST
ANOVA Table
Example: breaks by tension in warpbreaks data
How to do it with R
the aov function in base R
Remarks
- constant variance
- normality assumption
- multi-way ANOVA
- balanced sample sizes
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You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:
A. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission. B. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement. C. State on the Title page the name of the publisher of the Modified Version, as the publisher. D. Preserve all the copyright notices of the Document. E. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices. F. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below. G. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document's license notice. H. Include an unaltered copy of this License. I. Preserve the section Entitled "History", Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled "History" in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence. J. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the "History" section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission. K. For any section Entitled "Acknowledgements" or "Dedications", Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein. L. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles. M. Delete any section Entitled "Endorsements". Such a section may not be included in the Modified Version. N. Do not retitle any existing section to be Entitled "Endorsements" or to conflict in title with any Invariant Section. O. Preserve any Warranty Disclaimers.
If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version's license notice. These titles must be distinct from any other section titles.
You may add a section Entitled "Endorsements", provided it contains nothing but endorsements of your Modified Version by various parties–for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.
You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.
The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.
- COMBINING DOCUMENTS
You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.
The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.
In the combination, you must combine any sections Entitled "History" in the various original documents, forming one section Entitled "History"; likewise combine any sections Entitled "Acknowledgements", and any sections Entitled "Dedications". You must delete all sections Entitled "Endorsements".
- COLLECTIONS OF DOCUMENTS
You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.
You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.
- AGGREGATION WITH INDEPENDENT WORKS
A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an "aggregate" if the copyright resulting from the compilation is not used to limit the legal rights of the compilation's users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.
If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document's Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.
- TRANSLATION
Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.
If a section in the Document is Entitled "Acknowledgements", "Dedications", or "History", the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.
- TERMINATION
You may not copy, modify, sublicense, or distribute the Document except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense, or distribute it is void, and will automatically terminate your rights under this License.
However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.
Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.
Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, receipt of a copy of some or all of the same material does not give you any rights to use it.
- FUTURE REVISIONS OF THIS LICENSE
The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.
Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License "or any later version" applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. If the Document specifies that a proxy can decide which future versions of this License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Document.
- RELICENSING
"Massive Multiauthor Collaboration Site" (or "MMC Site") means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works. A public wiki that anybody can edit is an example of such a server. A "Massive Multiauthor Collaboration" (or "MMC") contained in the site means any set of copyrightable works thus published on the MMC site.
"CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0 license published by Creative Commons Corporation, a not-for-profit corporation with a principal place of business in San Francisco, California, as well as future copyleft versions of that license published by that same organization.
"Incorporate" means to publish or republish a Document, in whole or in part, as part of another Document.
An MMC is "eligible for relicensing" if it is licensed under this License, and if all works that were first published under this License somewhere other than this MMC, and subsequently incorporated in whole or in part into the MMC, (1) had no cover texts or invariant sections, and (2) were thus incorporated prior to November 1, 2008.
The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing.
ADDENDUM: How to use this License for your documents
To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:
Copyright (c) YEAR YOUR NAME. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".
If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with…Texts." line with this:
with the Invariant Sections being LIST THEIR TITLES, with the Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.
If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.
If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.
Date: 2010-12-03 15:08:39 EST
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