2 - Exponential-Polynomial-Trigonometric (2-EPT) Probability Density Functions
2-EPT Probability Density Functions are defined as the class of Probability Density Functions with strictly proper rational Characteristic Functions. 2-EPT densities can be represented by the triple (A, b, c) called the realization of the density. Much of the literature assumes the use of minimal realizations. Unlike phase-type distributions or matrix analytic functions the 2-EPT density functions are defined on the whole real line. It can be seen that the class of 2-EPT densities is closed under many operations. 2-EPT distributions form a flexible class of density functions which can be generalised to include a pointmass at zero. Under a certain parameter restriction the Variance Gamma density is shown to be 2-EPT. Examples in the literature demonstrate the benefits of adopting a 2-EPT approach for financial modelling purposes.
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