Bivariate distributions characterized by one family of conditionals and conditional percentile or mode functions |
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Authors: | Barry C. Arnold, Enrique Castillo,Jos Marí a Sarabia |
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Affiliation: | aDepartment of Statistics, University of California, Riverside, USA;bDepartment of Applied Mathematics and Computational Sciences,Universities of Cantabria and Castilla-La Mancha, Spain;cDepartment of Economics, University of Cantabria, Spain |
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Abstract: | 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. |
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Keywords: | 62H05 60E05 |
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