Multivariate Random Events Driven by Truncated Exponential Observations
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Authors
Chastain, Robert Pierce
Issue Date
2025
Type
Dissertation
Language
en_US
Keywords
counting distribution , geometric distribution , multivariate distribution , random sum , truncated exponential distribution
Alternative Title
Abstract
In this manuscript we build a general multivariate framework for characterizing stochasticepisodes driven by Truncated Exponential (TE ) observations. The TE model, which admits
values between zero and an upper bound δ, has applications in a wide range of fields including
ecology, seismology, finance, and physics. We develop three general frameworks for episode
characterization based on the total magnitude of the observations, the maximum observation,
and the duration of an episode.
The characterization of episodes is conducted in three separate but related models. The first
is a bivariate random vector based on the magnitude and duration. The second is a bivariate
model including the maximum and duration. The final characterization comes through a
trivariate model including magnitude, maximum, and duration. In all models the duration
is any arbitrary positive discrete random variable which provides a flexible framework for
modeling episodes driven by TE observations without requiring a specific distribution of
duration.
Finally, a new R package was developed and used to apply these models in modeling currency
exchange rate data. The results showed an excellent fit with the data demonstrating the
applicability of these models.