School of Mathematics and Statistics

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Browsing School of Mathematics and Statistics by Author "Arnold, Barry C."
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    All Conditional Distributions for Y Given X that are Compatible with a Given Conditional Distribution for X Given Y
    ( 2020-01-01) Arnold, Barry C. ; Manjunath, B. G.
    For a given conditional distribution for X given Y, it is important to identify the class of all conditional distributions for Y given X such that there exists at least one bivariate distribution with the given particular conditional densities. Such problems are addressed as dealing with “compatibility” of two conditional distributions. In the present note our goal is to identify all possible conditional densities for Y given X that are compatible with the given family of distributions of X given Y.
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    Statistical inference for distributions with one Poisson conditional
    ( 2021-01-01) Arnold, Barry C. ; Manjunath, B. G.
    It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals. However, it is known, from research on conditionally specified models, that Poisson marginals will be encountered, together with both conditionals being of the Poisson form, only in the case in which the variables are independent. In order to have a flexible dependent bivariate model with some Poisson components, in the present article, we will be focusing on bivariate distributions with one marginal and the other family of conditionals being of the Poisson form. Such distributions are called Pseudo-Poisson distributions. We discuss distributional features of such models, explore inferential aspects and include an example of applications of the Pseudo-Poisson model to sets of over-dispersed data.