When we try to use copulas for modeling discretely distributed random vectors, we encounter quite a few problems. One of them is the lack of uniqueness, which leads into confusion about what sort of objects we are dealing with. The problem of unidentifiability will be quantified by introducing two copulas known as Carley’s bounds and their measures of concordance and separately as a function of the flatness of the margins. The values of copulas derived form discrete cases and the values of their measures of concordance are contained inside the intervals of Carley’s bounds and measures of the bounds respectively. In continuous cases we have equivalence relations between copulas, measures of concordance and functional dependencies, but sadly many of them do not translate into discrete ones and some hold only one way. This will be shown through examples. One of the reasons for difficulties in discrete cases arises from non-zero probability of encountering ties, which we’ll try to correct by introducing modified concordance measures. We will list some of the dependency relations that do in fact translate from copulas into discretely distributed random vectors. They will show us, that even when dealing with discrete distributions, copulas still retain some of their use. We’ll use simulations to demonstrate the before mentioned problems and problems of estimating the dependance parameter.
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