Determining the lifetime distribution using fractional moments with maximum entropy.
Heliyon
; 10(15): e35250, 2024 Aug 15.
Article
em En
| MEDLINE
| ID: mdl-39170474
ABSTRACT
Here we propose a model-free, non-parametric method to solve an ill-posed inverse problem arising in several fields. It consists of determining a probability density of the lifetime, or the probability of survival of an individual, from the knowledge of the fractional moments of its probability distribution. The two problems are related, but they are different because of the natural normalization condition in each case. We provide a maximum entropy based approach to solve both problems. This problem provides a concrete framework to analyze an interesting problem in the theory of exponential models for probability densities. The central issue that comes up concerns the choice of the fractional moments and their number. We find that there are many possible choices that lead to solutions compatible with the data but in all of them, no more than four moments are necessary. The fact that a given data set can be accurately described by different exponential families poses a challenging problem for the model builder when attaching theoretical meaning to the resulting exponential density.
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Heliyon
Ano de publicação:
2024
Tipo de documento:
Article
País de afiliação:
Venezuela
País de publicação:
Reino Unido