Stable distribution (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Stable distribution" in English language version.

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21doi.org

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american.edu

academic2.american.edu

Nolan, John P. "Stable Distributions – Models for Heavy Tailed Data" (PDF). Archived from the original (PDF) on 2011-07-17. Retrieved 2009-02-21.

archive.org

Zolotarev, V. M. (1986). One-Dimensional Stable Distributions. American Mathematical Society. ISBN 978-0-8218-4519-6.

arxiv.org

Penson, K. A.; Górska, K. (2010-11-17). "Exact and Explicit Probability Densities for One-Sided Lévy Stable Distributions". Physical Review Letters. 105 (21): 210604. arXiv:1007.0193. Bibcode:2010PhRvL.105u0604P. doi:10.1103/PhysRevLett.105.210604. PMID 21231282. S2CID 27497684.

crcpress.com

Samorodnitsky, G.; Taqqu, M.S. (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. CRC Press. ISBN 9780412051715.
Janicki, Aleksander; Weron, Aleksander (1994). Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes. CRC Press. ISBN 9780824788827.

doi.org

Mandelbrot, B. (1960). "The Pareto–Lévy Law and the Distribution of Income". International Economic Review. 1 (2): 79–106. doi:10.2307/2525289. JSTOR 2525289.
Mandelbrot, B. (1961). "Stable Paretian Random Functions and the Multiplicative Variation of Income". Econometrica. 29 (4): 517–543. doi:10.2307/1911802. JSTOR 1911802.
Mandelbrot, B. (1963). "The Variation of Certain Speculative Prices". The Journal of Business. 36 (4): 394–419. doi:10.1086/294632. JSTOR 2350970.
Fama, Eugene F. (1963). "Mandelbrot and the Stable Paretian Hypothesis". The Journal of Business. 36 (4): 420–429. doi:10.1086/294633. JSTOR 2350971.
Mandelbrot, B. (1963). "New methods in statistical economics". The Journal of Political Economy. 71 (5): 421–440. doi:10.1086/258792. S2CID 53004476.
Voit, Johannes (2005). Balian, R; Beiglböck, W; Grosse, H; Thirring, W (eds.). The Statistical Mechanics of Financial Markets – Springer. Texts and Monographs in Physics. Springer. doi:10.1007/b137351. ISBN 978-3-540-26285-5.
Nolan, John P. (2020). Univariate stable distributions, Models for Heavy Tailed Data. Springer Series in Operations Research and Financial Engineering. Switzerland: Springer. doi:10.1007/978-3-030-52915-4. ISBN 978-3-030-52914-7. S2CID 226648987.
Nolan, John P. (1997). "Numerical calculation of stable densities and distribution functions". Communications in Statistics. Stochastic Models. 13 (4): 759–774. doi:10.1080/15326349708807450. ISSN 0882-0287.
Penson, K. A.; Górska, K. (2010-11-17). "Exact and Explicit Probability Densities for One-Sided Lévy Stable Distributions". Physical Review Letters. 105 (21): 210604. arXiv:1007.0193. Bibcode:2010PhRvL.105u0604P. doi:10.1103/PhysRevLett.105.210604. PMID 21231282. S2CID 27497684.
Zolotarev, V. (1995). "On Representation of Densities of Stable Laws by Special Functions". Theory of Probability and Its Applications. 39 (2): 354–362. doi:10.1137/1139025. ISSN 0040-585X.
Peach, G. (1981). "Theory of the pressure broadening and shift of spectral lines". Advances in Physics. 30 (3): 367–474. Bibcode:1981AdPhy..30..367P. doi:10.1080/00018738100101467. ISSN 0001-8732.
Pollard, Howard (1946). "Representation of e^{-x^\lambda} As a Laplace Integral". Bull. Amer. Math. Soc. 52: 908. doi:10.1090/S0002-9904-1946-08672-3.
McCulloch, J Huston (1986). "Simple consistent estimators of stable distribution parameters" (PDF). Communications in Statistics. Simulation and Computation. 15: 1109–1136. doi:10.1080/03610918608812563.
Chambers, J. M.; Mallows, C. L.; Stuck, B. W. (1976). "A Method for Simulating Stable Random Variables". Journal of the American Statistical Association. 71 (354): 340–344. doi:10.1080/01621459.1976.10480344. ISSN 0162-1459.
Misiorek, Adam; Weron, Rafał (2012). Gentle, James E.; Härdle, Wolfgang Karl; Mori, Yuichi (eds.). Heavy-Tailed Distributions in VaR Calculations (PDF). Springer Handbooks of Computational Statistics. Springer Berlin Heidelberg. pp. 1025–1059. doi:10.1007/978-3-642-21551-3_34. ISBN 978-3-642-21550-6.
Weron, Rafał (1996). "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables". Statistics & Probability Letters. 28 (2): 165–171. CiteSeerX 10.1.1.46.3280. doi:10.1016/0167-7152(95)00113-1. S2CID 9500064.
Mantegna, Rosario Nunzio (1994). "Fast, accurate algorithm for numerical simulation of Lévy stable stochastic processes". Physical Review E. 49 (5): 4677–4683. Bibcode:1994PhRvE..49.4677M. doi:10.1103/PhysRevE.49.4677. PMID 9961762.
Janicki, Aleksander; Kokoszka, Piotr (1992). "Computer investigation of the Rate of Convergence of Lepage Type Series to α-Stable Random Variables". Statistics. 23 (4): 365–373. doi:10.1080/02331889208802383. ISSN 0233-1888.
Garoni, T. M.; Frankel, N. E. (2002). "Lévy flights: Exact results and asymptotics beyond all orders". Journal of Mathematical Physics. 43 (5): 2670–2689. Bibcode:2002JMP....43.2670G. doi:10.1063/1.1467095.
Hopcraft, K. I.; Jakeman, E.; Tanner, R. M. J. (1999). "Lévy random walks with fluctuating step number and multiscale behavior". Physical Review E. 60 (5): 5327–5343. Bibcode:1999PhRvE..60.5327H. doi:10.1103/physreve.60.5327. PMID 11970402.
Zaliapin, I. V.; Kagan, Y. Y.; Schoenberg, F. P. (2005). "Approximating the Distribution of Pareto Sums". Pure and Applied Geophysics. 162 (6): 1187–1228. Bibcode:2005PApGe.162.1187Z. doi:10.1007/s00024-004-2666-3. S2CID 18754585.

escholarship.org

Zaliapin, I. V.; Kagan, Y. Y.; Schoenberg, F. P. (2005). "Approximating the Distribution of Pareto Sums". Pure and Applied Geophysics. 162 (6): 1187–1228. Bibcode:2005PApGe.162.1187Z. doi:10.1007/s00024-004-2666-3. S2CID 18754585.

harvard.edu

ui.adsabs.harvard.edu

Penson, K. A.; Górska, K. (2010-11-17). "Exact and Explicit Probability Densities for One-Sided Lévy Stable Distributions". Physical Review Letters. 105 (21): 210604. arXiv:1007.0193. Bibcode:2010PhRvL.105u0604P. doi:10.1103/PhysRevLett.105.210604. PMID 21231282. S2CID 27497684.
Peach, G. (1981). "Theory of the pressure broadening and shift of spectral lines". Advances in Physics. 30 (3): 367–474. Bibcode:1981AdPhy..30..367P. doi:10.1080/00018738100101467. ISSN 0001-8732.
Mantegna, Rosario Nunzio (1994). "Fast, accurate algorithm for numerical simulation of Lévy stable stochastic processes". Physical Review E. 49 (5): 4677–4683. Bibcode:1994PhRvE..49.4677M. doi:10.1103/PhysRevE.49.4677. PMID 9961762.
Garoni, T. M.; Frankel, N. E. (2002). "Lévy flights: Exact results and asymptotics beyond all orders". Journal of Mathematical Physics. 43 (5): 2670–2689. Bibcode:2002JMP....43.2670G. doi:10.1063/1.1467095.
Hopcraft, K. I.; Jakeman, E.; Tanner, R. M. J. (1999). "Lévy random walks with fluctuating step number and multiscale behavior". Physical Review E. 60 (5): 5327–5343. Bibcode:1999PhRvE..60.5327H. doi:10.1103/physreve.60.5327. PMID 11970402.
Zaliapin, I. V.; Kagan, Y. Y.; Schoenberg, F. P. (2005). "Approximating the Distribution of Pareto Sums". Pure and Applied Geophysics. 162 (6): 1187–1228. Bibcode:2005PApGe.162.1187Z. doi:10.1007/s00024-004-2666-3. S2CID 18754585.

jstor.org

Mandelbrot, B. (1960). "The Pareto–Lévy Law and the Distribution of Income". International Economic Review. 1 (2): 79–106. doi:10.2307/2525289. JSTOR 2525289.
Mandelbrot, B. (1961). "Stable Paretian Random Functions and the Multiplicative Variation of Income". Econometrica. 29 (4): 517–543. doi:10.2307/1911802. JSTOR 1911802.
Mandelbrot, B. (1963). "The Variation of Certain Speculative Prices". The Journal of Business. 36 (4): 394–419. doi:10.1086/294632. JSTOR 2350970.
Fama, Eugene F. (1963). "Mandelbrot and the Stable Paretian Hypothesis". The Journal of Business. 36 (4): 420–429. doi:10.1086/294633. JSTOR 2350971.
Le Cam, L. (February 1986). "The Central Limit Theorem around 1935". Statistical Science. 1 (1): 78–91. JSTOR 2245503.

nih.gov

pubmed.ncbi.nlm.nih.gov

Penson, K. A.; Górska, K. (2010-11-17). "Exact and Explicit Probability Densities for One-Sided Lévy Stable Distributions". Physical Review Letters. 105 (21): 210604. arXiv:1007.0193. Bibcode:2010PhRvL.105u0604P. doi:10.1103/PhysRevLett.105.210604. PMID 21231282. S2CID 27497684.
Mantegna, Rosario Nunzio (1994). "Fast, accurate algorithm for numerical simulation of Lévy stable stochastic processes". Physical Review E. 49 (5): 4677–4683. Bibcode:1994PhRvE..49.4677M. doi:10.1103/PhysRevE.49.4677. PMID 9961762.
Hopcraft, K. I.; Jakeman, E.; Tanner, R. M. J. (1999). "Lévy random walks with fluctuating step number and multiscale behavior". Physical Review E. 60 (5): 5327–5343. Bibcode:1999PhRvE..60.5327H. doi:10.1103/physreve.60.5327. PMID 11970402.

nottingham.ac.uk

eprints.nottingham.ac.uk

Lee, Wai Ha (2010). Continuous and discrete properties of stochastic processes. PhD thesis, University of Nottingham.

ohio-state.edu

asc.ohio-state.edu

McCulloch, J Huston (1986). "Simple consistent estimators of stable distribution parameters" (PDF). Communications in Statistics. Simulation and Computation. 15: 1109–1136. doi:10.1080/03610918608812563.

projecteuclid.org

Pollard, Howard (1946). "Representation of e^{-x^\lambda} As a Laplace Integral". Bull. Amer. Math. Soc. 52: 908. doi:10.1090/S0002-9904-1946-08672-3.

psu.edu

citeseerx.ist.psu.edu

Weron, Rafał (1996). "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables". Statistics & Probability Letters. 28 (2): 165–171. CiteSeerX 10.1.1.46.3280. doi:10.1016/0167-7152(95)00113-1. S2CID 9500064.

pwr.wroc.pl

im.pwr.wroc.pl

Misiorek, Adam; Weron, Rafał (2012). Gentle, James E.; Härdle, Wolfgang Karl; Mori, Yuichi (eds.). Heavy-Tailed Distributions in VaR Calculations (PDF). Springer Handbooks of Computational Statistics. Springer Berlin Heidelberg. pp. 1025–1059. doi:10.1007/978-3-642-21551-3_34. ISBN 978-3-642-21550-6.

randomservices.org

Siegrist, Kyle. "Stable Distributions". www.randomservices.org. Retrieved 2018-10-18.

semanticscholar.org

api.semanticscholar.org

Mandelbrot, B. (1963). "New methods in statistical economics". The Journal of Political Economy. 71 (5): 421–440. doi:10.1086/258792. S2CID 53004476.
Nolan, John P. (2020). Univariate stable distributions, Models for Heavy Tailed Data. Springer Series in Operations Research and Financial Engineering. Switzerland: Springer. doi:10.1007/978-3-030-52915-4. ISBN 978-3-030-52914-7. S2CID 226648987.
Penson, K. A.; Górska, K. (2010-11-17). "Exact and Explicit Probability Densities for One-Sided Lévy Stable Distributions". Physical Review Letters. 105 (21): 210604. arXiv:1007.0193. Bibcode:2010PhRvL.105u0604P. doi:10.1103/PhysRevLett.105.210604. PMID 21231282. S2CID 27497684.
Weron, Rafał (1996). "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables". Statistics & Probability Letters. 28 (2): 165–171. CiteSeerX 10.1.1.46.3280. doi:10.1016/0167-7152(95)00113-1. S2CID 9500064.
Zaliapin, I. V.; Kagan, Y. Y.; Schoenberg, F. P. (2005). "Approximating the Distribution of Pareto Sums". Pure and Applied Geophysics. 162 (6): 1187–1228. Bibcode:2005PApGe.162.1187Z. doi:10.1007/s00024-004-2666-3. S2CID 18754585.

ssrn.com

Lihn, Stephen (2017). "A Theory of Asset Return and Volatility Under Stable Law and Stable Lambda Distribution". SSRN.

unt.edu

library.unt.edu

Leddon, D., A statistical Study of Hard X-Ray Solar Flares

web.archive.org

Nolan, John P. "Stable Distributions – Models for Heavy Tailed Data" (PDF). Archived from the original (PDF) on 2011-07-17. Retrieved 2009-02-21.

wiley.com

eu.wiley.com

Rachev, Svetlozar T.; Mittnik, Stefan (2000). Stable Paretian Models in Finance. Wiley. ISBN 978-0-471-95314-2.

worldcat.org

search.worldcat.org

Lévy, Paul (1925). Calcul des probabilités. Paris: Gauthier-Villars. OCLC 1417531.
Nolan, John P. (1997). "Numerical calculation of stable densities and distribution functions". Communications in Statistics. Stochastic Models. 13 (4): 759–774. doi:10.1080/15326349708807450. ISSN 0882-0287.
Zolotarev, V. (1995). "On Representation of Densities of Stable Laws by Special Functions". Theory of Probability and Its Applications. 39 (2): 354–362. doi:10.1137/1139025. ISSN 0040-585X.
Peach, G. (1981). "Theory of the pressure broadening and shift of spectral lines". Advances in Physics. 30 (3): 367–474. Bibcode:1981AdPhy..30..367P. doi:10.1080/00018738100101467. ISSN 0001-8732.
Chambers, J. M.; Mallows, C. L.; Stuck, B. W. (1976). "A Method for Simulating Stable Random Variables". Journal of the American Statistical Association. 71 (354): 340–344. doi:10.1080/01621459.1976.10480344. ISSN 0162-1459.
Janicki, Aleksander; Kokoszka, Piotr (1992). "Computer investigation of the Rate of Convergence of Lepage Type Series to α-Stable Random Variables". Statistics. 23 (4): 365–373. doi:10.1080/02331889208802383. ISSN 0233-1888.