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Distribution Function, Probability Generating Function and Archimedean Generator
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Archimedean copulas form a very wide subclass of symmetric copulas. Most of the popular copulas are members of the Archimedean copulas. These copulas are obtained using real functions known as Archimedean generators. In this paper, we observe that under certain conditions the cumulative distribution functions on (0, 1) and probability generating functions can be used as Archimedean generators. It is shown that most of the well-known Archimedean copulas can be generated using such distributions. Further, we introduced new Archimedean copulas.
Title: Distribution Function, Probability Generating Function and Archimedean Generator
Description:
Archimedean copulas form a very wide subclass of symmetric copulas.
Most of the popular copulas are members of the Archimedean copulas.
These copulas are obtained using real functions known as Archimedean generators.
In this paper, we observe that under certain conditions the cumulative distribution functions on (0, 1) and probability generating functions can be used as Archimedean generators.
It is shown that most of the well-known Archimedean copulas can be generated using such distributions.
Further, we introduced new Archimedean copulas.
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