Expanding the Statistical Flowgraph Model Framework to Use Any Transition Distribution

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Abstract Historically, parametric statistical flowgraph models (SFGMs) have exclusively used distributions with moment generating functions (MGFs). This is a significant limitation because it does not allow the use of some common distributions. This paper extends SFGM methodology by using the mathematical construct of a complex Laplace transform in lieu of MGFs. This extension enables modeling all “smooth” densities in SFGMs. We demonstrate this method using an illustrative and a real data example; both the frequentist and Bayesian approaches are considered. This enhancement of parametric SFGMs notably extends their use and flexibility. R-code is available from the authors.