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

AI-powered answer engines are inherently non-deterministic: identical queries submitted at different times can produce different responses and cite different sources. Despite this stochastic behavior, current approaches to measuring domain visibility in generative search typically rely on single-run point estimates of citation share and prevalence, implicitly treating them as fixed values. This paper argues that citation visibility metrics should be treated as sample estimators of an underlying response distribution rather than fixed values. We conduct an empirical study of citation variability across three generative search platforms--Perplexity Search, OpenAI SearchGPT, and Google Gemini--using repeated sampling across three consumer product topics. Two sampling regimes are employed: daily collections over nine days and high-frequency sampling at ten-minute intervals. We show that citation distributions follow a power-law form and exhibit substantial variability across repeated samples. Bootstrap confidence intervals reveal that many apparent differences between domains fall within the noise floor of the measurement process. Distribution-wide rank stability analysis further demonstrates that citation rankings are unstable across samples, not only among top-ranked domains but throughout the frequently cited domain set. These findings demonstrate that single-run visibility metrics provide a misleadingly precise picture of domain performance in generative search. We argue that citation visibility must be reported with uncertainty estimates and provide practical guidance for sample sizes required to achieve interpretable confidence intervals.