Bivariate distributions characterized by one family of conditionals and conditional percentile or mode functions

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• 作者：Barry C. Arnold ; Enrique Castillo ; José ; Marí ; a Sarabia
• 关键词：Conditional specification ; Farley– ; Gumbel– ; Morgenstern distribution ; Gumbel’ ; s bivariate logistic distribution ; Normal characterization ; Cauchy conditionals
• 刊名：Journal of Multivariate Analysis
• 出版年：2008
• 出版时间：August 2008
• 年：2008
• 卷：99
• 期：7
• 页码：1383-1392
• 全文大小：238 K

文摘

It is well known that full knowledge of all conditional distributions will typically serve to completely characterize a bivariate distribution. Partial knowledge will often suffice. For example, knowledge of the conditional distribution of X given Y and the conditional mean of Y given X is often adequate to determine the joint distribution of X and Y. In this paper, we investigate the extent to which a conditional percentile function or a conditional mode function (of Y given X), together with knowledge of the conditional distribution of X given Y will determine the joint distribution. Finally, using this methodology a new characterization of the classical bivariate normal distribution is given.