  Geyser eruption is one of the most popular signature attractions at the
Yellowstone National Park. The interdependence of geyser eruptions and impacts
of covariates are of interest to researchers in geyser studies. In this paper,
we propose a parametric covariate-adjusted recurrent event model for estimating
the eruption gap time. We describe a general bivariate recurrent event process,
where a bivariate lognormal distribution and a Gumbel copula with different
marginal distributions are used to model an interdependent dual-type event
system. The maximum likelihood approach is used to estimate model parameters.
The proposed method is applied to analyzing the Yellowstone geyser eruption
data for a bivariate geyser system and offers a deeper understanding of the
event occurrence mechanism of individual events as well as the system as a
whole. A comprehensive simulation study is conducted to evaluate the
performance of the proposed method.
