Special Continuous Probability Distributions

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


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.


Probability Density Continuous Random Variable Cauchy Distribution Total Decay Width Spectral Line Shape 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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