https://doi.org/10.1140/epjp/s13360-022-02625-7
Regular Article
Extending the applicability of the RVT technique for the randomized radioactive decay chain model
Departament de Matemàtiques, Universitat Jaume I, 12071, Castellón, Spain
Received:
27
March
2021
Accepted:
20
March
2022
Published online:
30
March
2022
In this paper, we improve the existing analysis on the randomized radioactive decay chain model based on Bateman master equations, by Hussein and Selim (2020). For a decay chain of three species of radionuclides, the authors derived the probability density function for the concentrations, by using the random variable transformation technique. We extend this application to the general solution of Bateman equations. The density function is expressed as an expectation, which has important implications for parametric density estimation. This may improve the classical kernel estimation when the random dimensionality is not low. Numerical examples are included, where the decay parameters and the initial concentrations are assigned different probability distributions.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
