Quantifying Uncertainty in AI Visibility: A Statistical Framework for Generative Search Measurement

The paper presents a statistical framework for measuring citation visibility in generative search, emphasizing the non-deterministic nature of AI-powered answer engines. It conducts an empirical study across three platforms—Perplexity Search, OpenAI SearchGPT, and Google Gemini—utilizing repeated sampling to reveal that citation distributions exhibit substantial variability and follow a power-law form. The findings highlight the inadequacy of single-run visibility metrics, advocating for the inclusion of uncertainty estimates in performance reporting to better inform practitioners on the reliability of citation rankings in generative search applications.