Probability theory and stochastic processes Independence Concept
Independent and identically distributed random variables
Summary
A family of random variables is independent and identically distributed (i.i.d.) when the variables are mutually independent and all have the same distribution. It is the standard model of repeated trials of one experiment. The node i.i.d. random variables gives the precise definition.
Where this leads
31 pages build on this one.
- Queueing theory
- Koksma–Hlawka inequality
- Boolean model
- Wigner semicircle law
- Wald–Wolfowitz optimality of the sequential probability ratio test
- Sequential probability ratio test
- Pickands–Balkema–De Haan theorem
- Donsker's theorem
- Wald's equation
- Monte Carlo integration
- Marchenko–Pastur law
- Glivenko–Cantelli theorem
- Berry–Esseen theorem
- Hewitt–Savage zero–one law
- Random walk as a difference equation
- Renewal theory
- Statistical learning theory
- Infinitely divisible distribution
- Autoregressive conditional heteroskedasticity
- Sanov's theorem
- Law of the iterated logarithm
- Cramér's theorem
- Pitman–Koopman–Darmois theorem
- Empirical process
- Stable distribution
- De Finetti's theorem
- Monte Carlo method
- Anderson localization
- Skorokhod's embedding theorem
- Exchangeable random variables
- Fisher–Tippett–Gnedenko theorem
Further reading
About this page
| Tag | 00MRN0FARV |
|---|---|
| URI | m2://00MRN0FARV |
| Aliases | iid, i-i-d, independent-identically-distributed |
| Kind | concept |
| Writing | W0 stub |
| MSC | 60A05 |
| Specializes | Independence of random variables |
| Same as |
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What links here
Definitions
Used by
- Queueing theory
- Boolean model
- Wigner semicircle law
- Wald–Wolfowitz optimality of the sequential probability ratio test
- Sequential probability ratio test
- Donsker's theorem
- Wald's equation
- Monte Carlo integration
- Marchenko–Pastur law
- Glivenko–Cantelli theorem
- Berry–Esseen theorem
- Hewitt–Savage zero–one law
- Random walk as a difference equation
- Renewal theory
- Statistical learning theory
- Infinitely divisible distribution
- Autoregressive conditional heteroskedasticity
- Sanov's theorem
- Law of the iterated logarithm
- Cramér's theorem
- Pitman–Koopman–Darmois theorem
- Empirical process
- Stable distribution
- De Finetti's theorem
- Monte Carlo method
- Anderson localization
- Exchangeable random variables
- Fisher–Tippett–Gnedenko theorem