Use of Exponential Functions in the Evaluations of Stochastic Variables in the Ionizing Radiation Field

Terman Frometa-Castillo

Abstract


To show that some deficiencies arisen can occur as result of owing to the stochastic processes/effects (SP/Es) in areas of ionizing radiations have not been probabilistically treated nor modeled, because they use exponential functions (EFs) derived from unnecessary differential equations (DEs) or unnecessary definition; and 2) to discuss some statistical models project (SMp) proposals of new probabilistic functions (PFs) that have probabilistic foundations, and will overcome the quoted problems.

The following results were obtained: 1) Determination of deficiencies due to use of EFs in evaluations of the following SP/Es: cell survival attenuation of radiation, radioactive decay and radioactivity; and 2) The SMp formulations for these SP/Es.

The previous SP/Es have not been probabilistically treated nor modelled, since they use EFs that are non-PFs, and some of them are derived from unnecessary solutions of DEs or unnecessary definition. These differential equations used in the derivations do not represent physic properties of the SP/Es, but are simply a mathematic property of the EFs modelling their respective SP/Es. The SMp proposes PFs that will be able to model SP/Es with simple and homogeneous functions using the three types of SP/Es. The SMp models will represent new PFs, where the probability of a random variable X is expressed as PX = p(y), instead of x; and the stochastic region is limited by two 0% and/or 100%-deterministic regions. The SMp treats the radioactivity as a SP/E SMp type P2, and considers there is no need of its current definition.


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DOI: https://doi.org/10.5539/apr.v10n3p34

Copyright (c) 2018 Terman Frometa-Castillo

License URL: http://creativecommons.org/licenses/by/4.0

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