Interval algorithm for random number generation
The problem of generating a random number with an arbitrary probability distribution by using a general biased M-coin is studied. An efficient and very simple algorithm based on the successive refinement of partitions of the unit interval (0, 1), which we call the interval algorithm, is proposed. A...
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| Veröffentlicht in: | IEEE transactions on information theory Jg. 43; H. 2; S. 599 - 611 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
IEEE
01.03.1997
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | The problem of generating a random number with an arbitrary probability distribution by using a general biased M-coin is studied. An efficient and very simple algorithm based on the successive refinement of partitions of the unit interval (0, 1), which we call the interval algorithm, is proposed. A fairly tight evaluation on the efficiency is given. Generalizations of the interval algorithm to the following cases are investigated: (1) output sequence is independent and identically distributed (i.i.d.); (2) output sequence is Markov; (3) input sequence is Markov; (4) input sequence and output sequence are both subject to arbitrary stochastic processes. |
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| AbstractList | The problem of generating a random number with an arbitrary probability distribution by using a general biased M-coin is studied. An efficient and very simple algorithm based on the successive refinement of partitions of the unit interval (0, 1), which we call the interval algorithm, is proposed. A fairly tight evaluation on the efficiency is given. Generalizations of the interval algorithm to the following cases are investigated: (1) output sequence is independent and identically distributed (i.i.d.); (2) output sequence is Markov; (3) input sequence is Markov; (4) input sequence and output sequence are both subject to arbitrary stochastic processes. The problem of generating a random number with an arbitrary probability distribution by using a general biased M-coin is studied. The problem of generating a random number with an arbitrary probability distribution by using a general biased M-coin is studied. An efficient and very simple algorithm based on the successive refinement of partitions of the unit interval (0, 1), which we call the interval algorithm, is proposed. A fairly tight evaluation on the efficiency is given. Generalizations of the interval algorithm to the following cases are investigated: (1) output sequence is independent and identically distributed (i.i.d.); (2) output sequence is Markov; (3) input sequence is Markov; (4) input sequence and output sequence are both subject to arbitrary stochastic processes |
| Author | Hoshi, M. Te Sun Hao |
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| Cites_doi | 10.1017/S001309150003460X 10.1214/aoms/1177697074 10.1109/18.532895 10.1007/BF02579167 10.1109/18.259659 10.1214/aoms/1177692552 10.1007/BF03007652 10.1147/rd.232.0149 10.1109/18.412679 10.1109/18.256486 10.1007/BF02760609 10.1214/aop/1176993384 10.1214/aos/1176348543 10.1002/j.1538-7305.1948.tb01338.x 10.2307/1971117 10.1002/0471200611 |
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| References | ref13 ref24 ref12 knuth (ref7) 1976 ref14 blum (ref6) 1986; 6 marshall (ref21) 1967 schur (ref20) 1923; 22 ref11 ref22 ref10 cover (ref17) 1991 ref2 csisza´r (ref23) 1981 keane (ref15) 1991 von neumann (ref1) 1951; 12 ref9 ref4 ref3 ref5 ahlswede (ref16) 1987 muirhead (ref19) 1903; 21 roche (ref8) 1992 shannon (ref18) 1948; 27 |
| References_xml | – volume: 21 start-page: 144 year: 1903 ident: ref19 article-title: some methods applicable to identities and inequalities of the symmetric algebraic functions of $n$ letters publication-title: Proc Edinburgh Math Soc doi: 10.1017/S001309150003460X – ident: ref2 doi: 10.1214/aoms/1177697074 – ident: ref9 doi: 10.1109/18.532895 – volume: 6 start-page: 97 year: 1986 ident: ref6 article-title: independent unbiased coin flips from a correlated biased source-a finite state markov chain publication-title: COMBINATORICA doi: 10.1007/BF02579167 – ident: ref22 doi: 10.1109/18.259659 – year: 1981 ident: ref23 publication-title: Information Theory Coding Theorems for Discrete Memoryless Systems – start-page: 177 year: 1967 ident: ref21 article-title: monotonicity of ratios of means and other applications of majorization publication-title: Inequalities – volume: 12 start-page: 36 year: 1951 ident: ref1 publication-title: Various techniques used in connection with random digits – ident: ref5 doi: 10.1214/aoms/1177692552 – volume: 22 start-page: 9 year: 1923 ident: ref20 article-title: u¨ber ein klasse von mittelbildungen mit anwendungen auf die determinatentheorie publication-title: Sitzungsberichte Berliner Math Ges – ident: ref12 doi: 10.1007/BF03007652 – ident: ref24 doi: 10.1147/rd.232.0149 – ident: ref11 doi: 10.1109/18.412679 – start-page: 35 year: 1991 ident: ref15 article-title: ergodic theory and subshifts of finite type publication-title: Ergodic Theory Symbolic Dynamics and Hyperbolic Spaces – ident: ref10 doi: 10.1109/18.256486 – ident: ref14 doi: 10.1007/BF02760609 – start-page: 357 year: 1976 ident: ref7 article-title: the complexity of nonuniform random number generation publication-title: Algorithms and Complexity New Directions and Results – ident: ref3 doi: 10.1214/aop/1176993384 – ident: ref4 doi: 10.1214/aos/1176348543 – year: 1992 ident: ref8 publication-title: Efficient generation of random variables from biased coins – year: 1987 ident: ref16 publication-title: Search Problems – volume: 27 start-page: 379 year: 1948 ident: ref18 article-title: prediction and entropy of printed english publication-title: Bell Syst Tech J doi: 10.1002/j.1538-7305.1948.tb01338.x – ident: ref13 doi: 10.2307/1971117 – year: 1991 ident: ref17 publication-title: Elements of Information Thoery doi: 10.1002/0471200611 |
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| Snippet | The problem of generating a random number with an arbitrary probability distribution by using a general biased M-coin is studied. An efficient and very simple... The problem of generating a random number with an arbitrary probability distribution by using a general biased M-coin is studied. |
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| SubjectTerms | Algorithms Arithmetic Entropy Information processing Markov processes Numbers Partitioning algorithms Probability distribution Random number generation Stochastic processes Sun Tellurium Upper bound |
| Title | Interval algorithm for random number generation |
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