Crystal Ball function

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Examples of the 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.

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