Alternative definitions of bivariate equilibrium distributions

作者：Navarro Jorge^*; Maria Sarabia Jose

来源：Journal of Statistical Planning and Inference, 2010, 140(7): 2046-2056.

DOI：10.1016/j.jspi.2010.01.044

• Exponential conditional distribution
• Gumbel type I exponential distribution
• Hazard gradient function
• Bivariate failure rate
• Stochastic orders

The concept of equilibrium distribution plays an important role in survival analysis, reliability and insurance studies. If we consider the problem of extending this concept to higher dimensions, we do not have a unique solution. In this paper, alternative definitions of bivariate equilibrium distributions are studied and proposed. The Navarro et al. (2006) proposal is considered and some new results are given. We continue with the Gupta and Sankaran's (1998) definition. Necessary and sufficient conditions for its existence are stated and a characterization theorem is given. As a third alternative, a new definition based on conditional specification is introduced and several results are obtained. Reliability properties of the different versions are studied.

• 出版日期2010-7