Extended q-Gaussian and q-exponential distributions from gamma random variables.
Phys Rev E Stat Nonlin Soft Matter Phys
; 91(5): 052113, 2015 May.
Article
en En
| MEDLINE
| ID: mdl-26066125
The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q-Gaussian and q-exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q-Gaussian and modified q-exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.
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Colección:
01-internacional
Base de datos:
MEDLINE
Tipo de estudio:
Clinical_trials
/
Prognostic_studies
Idioma:
En
Revista:
Phys Rev E Stat Nonlin Soft Matter Phys
Asunto de la revista:
BIOFISICA
/
FISIOLOGIA
Año:
2015
Tipo del documento:
Article
País de afiliación:
Argentina
Pais de publicación:
Estados Unidos