Crystal Ball function
The Crystal Ball function, named after the Crystal Ball Collaboration (hence the capitalized initial letters), is a probability density function commonly used to model various lossy processes in high-energy physics. It consists of a Gaussian core portion and a power-law low-end tail, below a certain threshold. The function itself and its first derivative are both continuous.
The Crystal Ball function is given by:
where
- ,
- ,
- ,
- ,
- .
(Skwarnicki 1986) is a normalization factor and , , and are parameters which are fitted with the data. erf is the error function.
External links
- J. E. Gaiser, Appendix-F Charmonium Spectroscopy from Radiative Decays of the J/Psi and Psi-Prime, Ph.D. Thesis, SLAC-R-255 (1982). (This is a 205-page document in .pdf form – the function is defined on p. 178.)
- M. J. Oreglia, A Study of the Reactions psi prime --> gamma gamma psi, Ph.D. Thesis, SLAC-R-236 (1980), Appendix D.
- T. Skwarnicki, A study of the radiative CASCADE transitions between the Upsilon-Prime and Upsilon resonances, Ph.D Thesis, DESY F31-86-02(1986), Appendix E.
- v
- t
- e
Probability distributions (list)
univariate
with finite support |
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with infinite support |
univariate
univariate
continuous- discrete |
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(joint)
- Discrete:
- Ewens
- multinomial
- Continuous:
- Dirichlet
- multivariate Laplace
- multivariate normal
- multivariate stable
- multivariate t
- normal-gamma
- Matrix-valued:
- LKJ
- matrix normal
- matrix t
- matrix gamma
- Wishart
- Univariate (circular) directional
- Circular uniform
- univariate von Mises
- wrapped normal
- wrapped Cauchy
- wrapped exponential
- wrapped asymmetric Laplace
- wrapped Lévy
- Bivariate (spherical)
- Kent
- Bivariate (toroidal)
- bivariate von Mises
- Multivariate
- von Mises–Fisher
- Bingham
and singular
- Degenerate
- Dirac delta function
- Singular
- Cantor
- Category
- Commons