- Random sequence
A random sequence is a kind of
stochastic process . In short, arandom sequence is asequence ofrandom variable s.Random sequences are essential in
statistics . The statistical analysis of anyexperiment usually begins with the words "let "X"1,...,"Xn" be independent random variables...". The easiest way to talk about a situation when you can choose to make new measurements is to assume that an infinite sequence {"Xi"} is given, and that successive stages of the experiment you look at the first "N" terms of the sequence. Also, the statement of thelaw of large numbers (essentially that the average of a number of observations converges to the mean value) involves an infinite sequence ofindependent identically-distributed random variables .Use of the term in algorithmic information theory
The term "random sequence" can also describe a finite sequence, or string, of random characters. (Though not universal, computer scientists generally refer to an infinite sequence of characters or digits as a "sequence", and a finite sequence of characters or digits as a "string".)
Algorithmic information theory defines a random string as one that cannot be produced from any computer program that is shorter than the string (Chaitin-Kolmogorov randomness ); i.e. a string whoseKolmogorov complexity is at least the length of the string. This is a different meaning from the usage of the term in statistics. Whereas statistical randomness refers to the "process" that produces the string (e.g. flipping a coin to produce each bit will randomly produce a string), algorithmic randomness refers to the "string itself". Algorithmic information theory separates random from nonrandom strings in a way that is relatively invariant to themodel of computation being used.An
algorithmically random sequence is an "infinite" sequence of characters, all of whose prefixes (except possibly a finite number of exceptions) are strings that are "close to" algorithmically random (their length is within a constant of their Kolmogorov complexity).References
* Per Martin-Löf. The Definition of Random Sequences. Information and Control, 9(6): 602-619,
1966 .ee also
*
Halton sequence
*Randomness
*Random number generator
*Statistical randomness
*Algorithmically random sequence
*Kolmogorov complexity External links
* [http://www.ciphersbyritter.com/RES/RANDTEST.HTM#vonNeumann63 Randomness tests by Terry Ritter]
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