Mathematical analysis of long tail economy using stochastic ranking processes

TL;DR

This paper introduces a mathematical approach to analyze the long tail distribution of sales in online retail, using stochastic ranking processes to estimate sales rate distributions from ranking data.

Contribution

It develops a new mathematical framework based on infinite particle limits of stochastic ranking processes for analyzing long tail sales data.

Findings

Successfully estimated Pareto slope parameter from Amazon.co.jp data.

Demonstrated the method's applicability to real online retail ranking data.

Provided a quantitative tool for long tail sales analysis.

Abstract

We present a new method of estimating the distribution of sales rates of, e.g., book titles at an online bookstore, from the time evolution of ranking data found at websites of the store. The method is based on new mathematical results on an infinite particle limit of the stochastic ranking process, and is suitable for quantitative studies of the long tail structure of online retails. We give an example of a fit to the actual data obtained from Amazon.co.jp, which gives the Pareto slope parameter of the distribution of sales rates of the book titles in the store.