Exploring empirical rank-frequency distributions longitudinally through a simple stochastic process

Area of Science:

• Complex Systems
• Data Science
• Statistical Modeling

Background:

• Rank-frequency distributions, like Zipf's law, are common across many scientific domains.
• Understanding and modeling these distributions is crucial for various fields.

Purpose of the Study:

• To simulate empirical rank-frequency distributions using a simplified stochastic cascade process.
• To make the modeling process accessible to non-mathematical experts.

Main Methods:

• Employed a stochastic cascade process to generate rank-frequency distributions.
• Focused on a simplified model to enhance mathematical accessibility.
• Simulated longitudinal variations through repeated trials of the process.

Main Results:

• The stochastic cascade process effectively models concave rank-frequency distributions and finite size effects.
• The model can approximate longitudinal rank variations.
• Empirical data showed less variation than the model, suggesting uncaptured longitudinal dependencies.

Conclusions:

• The simplified stochastic cascade process is a viable tool for modeling rank-frequency distributions.
• The model highlights the importance of considering longitudinal dependencies in empirical data.
• The approach offers practical applications for analyzing rank-frequency data.