The purpose of the study is to analyze the accounting equation and develop a new model, based on the dual concept of monetary units and the structure of assets and claims on assets. The analysis uses the identity and characteristic functions along with a coordinate transformation, to show that the assets-claims on assets relationship involves a change in claims on assets value. The identity function represents the dual concept of the monetary units and the characteristic function relates both sides of the accounting equation. A different number of dimensions arise on each side of the equation, and a coordinate transformation is applied to have both sides of the equation with two dimensions. This transformation results in a change in the value of claims on assets. Finally, a computation using a probability density function or kernel is proposed to allow approaching the coefficients of the new model. Results show that the accounting equation consists of a series of addition functions to sum up all the monetary units and that a new model with a probability density function can help in the analysis of the assets-claims on assets relationship.