<p>We introduce a new bivariate distribution for modeling two dimensional data supported on the unit square. The one dimensional marginals of this bivariate distribution follow the univariate Power Function Distributions (PFDs), leading us to name this new distribution the <i>Bivariate Power Function Distribution</i> (BPFD). The BPFD is constructed using a common-shock mechanism analogous to the Marshall–Olkin bivariate exponential model. Marshall–Olkin and related extensions are three parameter models, in which the common shock affects both components symmetrically through the same parameter, which leads to a positive probability of ties. By contrast, the BPFD is a four parameter model that allows the shared shock to impact the two variables asymmetrically and, for almost all parameter choices, produces no ties. The only exception arises when a specific pair of parameters coincide, in which case ties occur. We derive the model’s stochastic properties, present its copula representation, and obtain various closed form dependence measures. Since the joint density is not available in closed form, we propose a modified Method of Moments framework for parameter estimation. The finite sample performance of the estimators is assessed via simulation studies. Finally, we illustrate the model on two real datasets: one containing ties, and other containing no ties, demonstrating that the BPFD can accommodate both settings, in contrast to the classical Marshall–Olkin models which requires the presence of ties.</p>