Variability comparisons for some mixture models with stochastic environments in biosciences and engineering

  • Laureano F. Escudero
  • Eva María Ortega
  • José Alonso
Original Paper


Statistical modeling of the dependence within applied stochastic models has become an important goal in many fields of science, since Pearson’s correlation does not provide a complete description of the dependence structure of the random variables, being strongly affected from extreme endpoints, and correlation zero does not imply independence, except in the case of multivariate normal distributions. The construction of bounds for the variability of the distributions of some applied stochastic models when there is only partial information on the dependence structure of the models is the main purpose of this paper. We consider stochastic models in engineering, hydrology, and biosciences, that are defined by mixtures with stochastic environmental parameters. We study stochastic monotonicity and directional convexity properties of some functionals of random variables that are used to define these models. Variability comparisons between the mixture models in terms of the dependence between the stochastic environments are obtained. Stochastic bounds and examples are derived from modeling the dependence structure by some known notions.


Stochastic orders Dependence Variability Bounds Stochastic directional convexity Environmental modeling Biology Hydrology Communication networks Engineering Risk management Medicine 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Laureano F. Escudero
    • 1
  • Eva María Ortega
    • 2
  • José Alonso
    • 3
  1. 1.Dpto. Estadística e Investigación OperativaUniversidad Rey Juan CarlosMóstoles (Madrid)Spain
  2. 2.Centro de Investigación OperativaUniversidad Miguel HernándezOrihuela (Alicante)Spain
  3. 3.Servicio de RadiologíaHospital Universitario Virgen ArrixacaEl Palmar (Murcia)Spain

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