Mixture and Exponential Arcs on Generalized Statistical Manifold

Area of Science:

• Statistics
• Differential Geometry

Background:

• Statistical manifolds provide a geometric framework for statistical models.
• Understanding arcs and their properties is crucial for analyzing statistical structures.

Purpose of the Study:

• To generalize the concept of the mixture arc on statistical manifolds.
• To establish a well-defined generalization of the open exponential arc and investigate its properties.
• To utilize a φ-family of distributions for a general statistical model.

Main Methods:

• Investigating the mixture arc on generalized statistical manifolds.
• Defining and analyzing the generalized open exponential arc.
• Employing a φ-family of distributions for model description.

Main Results:

• A well-defined generalization of the mixture arc is established.
• Properties of the generalized open exponential arc are provided.
• The φ-family of distributions serves as a framework for the general statistical model.

Conclusions:

• The generalization of the mixture arc is mathematically sound.
• The study enhances the understanding of geometric structures in statistical modeling.
• The φ-family provides a flexible approach to statistical manifold analysis.