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The exponential-normal form and its application to ultra high energy cascades investigation

Author

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  • Kirillov A. A.

    (D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow 119992, Russia. Email: krl@dec1.sinp.msu.ru)

  • Kirillov I. A.

    (“Energoatom”, Moscow 109507, Ferganskaya str. 25, Moscow, Russia. Email: iakir@rambler.ru)

Abstract

The normalized exponential-normal form A · exp(–(x – c)2/(a(x – c) + 2b 2)) is an asymmetric distribution intermediate between the normal and exponential distributions. Some properties of the form are presented and some methods of approximation are suggested. Appropriate formulae and table are presented. The quality of original data defines the specific features of the methods. Application of the methods is illustrated by ultra high energy atmospheric showers investigation. The relation to the exponential and normal distributions makes the form useful and effective in applications.

Suggested Citation

  • Kirillov A. A. & Kirillov I. A., 2009. "The exponential-normal form and its application to ultra high energy cascades investigation," Monte Carlo Methods and Applications, De Gruyter, vol. 15(2), pages 107-133, January.
    • Handle: RePEc:bpj:mcmeap:v:15:y:2009:i:2:p:107-133:n:2
    DOI: 10.1515/MCMA.2009.006
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