Prompting Shapes the Statistical Tails of LLM ‐Generated Biomedical Data

We evaluate four large language models ( gpt‐4o , gpt‐4.1 , o3 , o4‐mini ) on six biomedically inspired tasks motivated by domains that often exhibit heavy‐tailed or strongly skewed behavior. We compare three prompt styles—Natural (N), Mixed (M), and Constrained (C)—that differ in distributional pressure; temperature and top‐ are varied where supported. The study is designed to quantify how prompt‐conditioned distributional pressure modulates the tail‐risk profile of generated numeric outputs, rather than to assess fidelity to an external biomedical ground‐truth distribution. Outliers are flagged using a stabilized MAD– rule (), and threshold robustness is summarized by the normalized area under outlier–threshold curves (nAURC). Tail behavior is assessed via complementary diagnostics (exceedances, high quantiles, Moors' kurtosis, and a secondary Pareto‐equivalent exceedance index), with uncertainty quantified using pooled binomial aggregation (Wilson/Newcombe intervals), logit‐based CIs for nAURC, dominance areas over threshold grids, and random‐effects meta‐analysis across problems. Three results emerge. (1) Prompt style is the primary driver of extremes: Under our evaluation criteria, Natural prompts yield the most conservative tail‐risk profile: they consistently minimize outlier rate and nAURC and produce the lightest tails. The ordering between Mixed and Constrained varies by model, while Constrained often produces heavier tails, as expected under explicit tail instructions. (2) These patterns persist across thresholds and problems: Natural robustly dominates both Mixed and Constrained in robustness‐curve dominance area, and meta‐analytic gaps in outlier share are consistently positive for C–N and M–N across models. (3) Sampling (temperature/top‐) modulates risk within a fixed (model, prompt) cell: effects are consistently positive for outlier incidence in our temperature contrasts and can be substantial in some settings (notably gpt‐4.1 under Natural prompting), but they do not overturn the qualitative prompt ordering in pooled summaries. Overall, prompt design is the most reliable lever for controlling outliers and heavy‐tail risk in LLM‐generated numeric data, with sampling parameters providing additional combination‐specific control. These conclusions apply most directly to the heavy‐tailed biomedical‐inspired settings studied here.