Talk:Crystal Ball function

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Latest comment: 6 years ago5 comments4 people in discussion

The proper name of the entry is "Crystal Ball (function)", since it is named after the Crystal Ball Collaboration, with Ball capitalized.

There appear to be some inaccuracies in this page.

1) in the plot shown to the right, the parameter "n" is not specified. Since I reproduced the function on my own, I think both "N" and "n" are equal to 1, but can not be positive.

2) the author did not specify how to reproduce the long tail to the right of the peak. I assume alpha can be both positive and negative, although when writing my own program I ended up switching the sign of (x-xave)/sigma by hand.

3) More generally, the author did not specify the limits for the free parameters of the function. For example, alpha should be both negative and positive but not zero. "n", I assume, is positive, as are N and sigma. xave should be unbound.

4) N is not a "true" normalization parameter, and it does not correspond to the true number of events in a histogram for example. —Preceding unsigned comment added by Gbli (talk • contribs) 15:40, 8 June 2009 (UTC)Reply

5) There is a problem with this function when n = 1. Then C goes to Inf so N goes to 0 (zero) whenever n = 1. Meaning that two plots are bogus. — Preceding unsigned comment added by Achitan (talk • contribs) 18:44, 30 April 2013 (UTC)Reply

Yeah, you're right. I'll talk to the author of the plots. -- UKoch (talk) 17:19, 9 May 2013 (UTC)Reply

6) I think this should be rewritten to address the concerns above. The issue is that the normalization factor, N, is not a necessary part of the Crystal Ball function. The function is defined without the factor this, but it will not be a proper pdf. If the function is required to be normalized, then you will find that N is only defined when n > 1 by carrying out the integration over all x. I assume that the plot was made using ROOT and it's implementation is such that N is not included or the integration is calculated numerically within some truncated domain. — Preceding unsigned comment added by Naodell (talk • contribs) 01:27, 8 May 2017 (UTC)Reply

Naodell, your words make a lot of sense to me. I'm going to change the article accordingly. -- UKoch (talk) 20:38, 12 May 2017 (UTC)Reply

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