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Special Continuous Probability Distributions

  • Simon ŠircaEmail author
Chapter
Part of the Graduate Texts in Physics book series (GTP)

Abstract

Particular continuous distributions encountered on a daily basis are discussed: the simplest uniform distribution, the exponential distribution characterizing the decay of unstable atoms and nuclei, the ubiquitous normal (Gauss) distribution in both its general and standardized form, the Maxwell velocity distribution in its vector and scalar form, the Pareto (power-law) distribution, and the Cauchy (Lorentz, Breit–Wigner) distribution suitable for describing spectral line shapes and resonances. Three further distributions are introduced (\(\chi ^2\)-, Student’s t- and F-distributions), predominantly used in problems of statistical inference based on samples. Generalizations of the exponential law to hypo- and hyper-exponential distributions are presented.

Keywords

Probability Density Continuous Random Variable Cauchy Distribution Total Decay Width Spectral Line Shape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    D.C. Montgomery, G.C. Runger, Applied Statistics and Probability for Engineers, 5th edn (John Wiley & Sons, New York, 2010)Google Scholar
  2. 2.
    G.H. Jowett, The exponential distribution and its applications. Inco. Stat. 8, 89 (1958)zbMATHGoogle Scholar
  3. 3.
    P.J. Aston, Is radioactive decay really exponential?, Europhys. Lett. 97 (2012) 52001. See also the reply C. A. Nicolaides, Comment on Is radioactive decay really exponential?. Europhys. Lett. 101, 42001 (2013)Google Scholar
  4. 4.
    R.G. Newton, Scattering Theory of Waves and Particles, 2nd edn (Springer-Verlag, Berlin, 1982)Google Scholar
  5. 5.
    E. Merzbacher, Quantum Mechanics, 3rd edn (Wiley & Sons Inc, New York, 1998)Google Scholar
  6. 6.
    M.L. Goldberger, K.M. Watson, Collision Theory, (John Wiley & Sons, New York 1964) (Chapter 8)Google Scholar
  7. 7.
    H. Poincaré, Calcul des Probabilités (Gauthier-Villars, Paris, 1912)zbMATHGoogle Scholar
  8. 8.
    WHO Global InfoBase team, The SuRF Report 2. Country-level data and comparable estimates. (World Health Organization, Geneva, Surveillance of chronic disease Risk Factors, 2005)Google Scholar
  9. 9.
    M.E.J. Newman, Power laws, Pareto distributions and Zipf’s law. Contemp. Phys. 46, 323 (2005)Google Scholar
  10. 10.
    A. Clauset, C.R. Shalizi, M.E.J. Newman, Power-law distributions in empirical data. SIAM Rev. 51, 661 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    M. Schroeder, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (W.H. Freeman, New York, 1991)zbMATHGoogle Scholar
  12. 12.
    J.W. Head, C.I. Fassett, S.J. Kadish, D.E. Smith, M.T. Zuber, G.A. Neumann, E. Mazarico, Global distribution of large lunar craters: implications for resurfacing and impactor populations. Science 329, 1504 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    S.J. Kadish, C.I. Fassett, J.W. Head, D.E. Smith, M.T. Zuber, G.A. Neumann, E. Mazarico, A Global Catalog of Large Lunar Crater (\(\ge 20\,{\rm {km}}\)) from the Lunar Orbiter Laser Altimeter. Lunar Plan. Sci. Conf., XLII, abstract 1006 (2011)Google Scholar
  14. 14.
    B.R. Dennis, L.E. Orwig, G.S. Kennard, G.J. Labow, R.A. Schwartz, A.R. Shaver, A.K. Tolbert, The Complete Hard X-ray Burst Spectrometer Event List, 1980–1989, NASA Technical Memorandum 4332 (NASA, 1991)Google Scholar
  15. 15.
    S. Bukvić, S. Djeniže, A. Srećković, Line broadening in the Si I, Si II, Si III, and Si IV spectra in the helium plasma, Astron. Astrophys. 508, 491 (2009)Google Scholar
  16. 16.
    Student [W.S. Gosset], The probable error of a mean. Biometrika 6, 1 (1908)Google Scholar
  17. 17.
    R. Jamnik, Verjetnostni račun (Mladinska knjiga, Ljubljana, 1971)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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