Abstract
Abstract
Many types of bounded data defined on the unit interval arise naturally as ratios of the form
$$X/(X + Y)$$
. In the existing literature, the main statistical models proposed for this type of bounded data are typically based on the assumption that the random variables
X
and
Y
are independent. However, this assumption is often unrealistic in practical applications, where
X
and
Y
tend to be correlated due to shared underlying mechanisms or common sources of variability. In this paper, we overcome such limitations and propose a model in which the marginal distributions of the two components are linked by a copula, leading to a more flexible and realistic representation of unit-interval data. In particular, in the proposed model,
X
and
Y
are dependent gamma random variables whose joint distribution is specified via Morgenstern’s bivariate distribution, allowing for positive and negative correlations between the components. The mathematical properties and practical applications are rigorously investigated. The resulting distribution exhibits a wide range of shapes, accommodating different degrees of skewness and, for some parameter configurations, more complex density structures. A Monte Carlo simulation study is carried out that shows the good performance of the maximum likelihood estimator in several scenarios of parameter choices. The potential and limitations of efficient likelihood-based computations are also discussed. We evaluate the effectiveness of the new model and its estimates in modeling real-world datasets related to economics.