Geodesic
General properties of probability density $A\cdot\exp(-(x-c)^2/(a(x-c)+2b^2))$
Matematičeskoe modelirovanie, Tome 16 (2004) no. 1, pp. 75-89.

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General properties (parametric scaling, mean value, variance, width, asymmetry) of probability density $A\cdot\exp(-(x-c)^2/(a(x-c)+2b^2))$ are investigated as a general cause of the normal and exponential ones. It is able to describe wider class of processes than just ones. Methods determination, visual interpretation and calculation its parameters are presented. One can operate with the distribution as well as with normal distribution. Formulae and example are adduced. 
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A. A. Kirillov; I. A. Kirillov. General properties of probability density $A\cdot\exp(-(x-c)^2/(a(x-c)+2b^2))$. Matematičeskoe modelirovanie, Tome 16 (2004) no. 1, pp. 75-89. http://geodesic.mathdoc.fr/item/MM_2004_16_1_a5/

[1] G. T. Zatsepin, V. A. Kuzmin, “O verkhnei granitse spektra kosmicheskikh luchei”, Pisma v ZhETF, 4:3 (1966), 114–116

[2] A. A. Kirillov, L. A. Kirillov, “Approximation of individual cascades with energies above GZK cut-off”, Proc. 27th Int. Cosmic Ray Conf., 2, Hamburg, 2001, 483–486 | MR

[3] B. V. Gnedenko, A. N. Kolmogorov, Predelnye raspredeleniya dlya summ nezavisimykh sluchainykh velichin, 264 s., Gostekhizdat, M., 1949 | MR

[4] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, T. 2, Perevod s angl. Yu. V. Prokhorova, Mir, M., 1967, 752 pp.

[5] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, GIFML, M., 1962, 1100 pp.

[6] A. A. Kirillov, L. A. Kirillov, “Appoximation of individual and mean cascades with energies above GZK cutoff”, Astroparticle Physics, 19:1 (2003), 101–112 | DOI | MR

[7] C. L. Pryke, “A comparative study of the depth of maximum of simulated air shower longitudinal profiles”, Astroparticle Physics, 14 (2001), 319–328 | DOI

[8] E. E. Antonov, L. G. Dedenko, A. A. Kirillov, T. M. Rozanova, G. F. Fedorova, E. Yu. Fedunin, “Proverka lorentsevskoi invariantnosti po nablyudeniyam prodolnogo razvitiya shirokikh atmosfernykh livnei pri sverkhvysokikh energiyakh”, Pisma v ZhETF, 73:9 (2001), 506–510

[9] L. G. Dedenko, A. A. Kirillov, G. F. Fedorova, “Description of cascades with energies above the GZK cut-off”, 18th European Cosmic Ray Symp. (Moscow), 2002, 56 pp.