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The probability density function for crystalball is:
f(x, \beta, m) = \begin{cases} N \exp(-x^2 / 2), &\text{for } x > -\beta\\ N A (B - x)^{-m} &\text{for } x \le -\beta \end{cases}
where A = (m / |\beta|)^m \exp(-\beta^2 / 2), B = m/|\beta| - |\beta| and N is a normalisation constant.
crystalball takes \beta > 0 and m > 1 as shape parameters. \beta defines the point where the pdf changes from a power-law to a Gaussian distribution. m is the power of the power-law tail.
Crystalball distribution
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