Speed heterogeneity and non-Gaussian transport in active particles: a survival-hazard framework

Non-Gaussian displacement statistics in active-particle systems are often associated with heterogeneity in particle motility. In this work, we develop an estimation-based statistical framework that links speed distributions inferred from experimental data to effective-diffusivity and displacement statistics in active Brownian particles (ABPs) and active particles with passive noise (APPs). Rayleigh, Weibull, and generalized gamma distributions are fitted by maximum likelihood to a sample of 53 representative speeds extracted from experimental cell trajectories, and the candidate models are compared using the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and the Kolmogorov-Smirnov statistic. The fitted distributions are further examined through their cumulative distribution, survival, hazard, and reversed-hazard functions, allowing the distinct contributions of slow and fast particles to the transport statistics to be characterized. The results show that the Weibull distribution provides the most efficient balance between goodness of fit and model complexity according to AIC and BIC, whereas the generalized gamma distribution yields a slightly smaller empirical discrepancy at the cost of an additional parameter. Propagating the fitted speed distributions through the quadratic diffusivity map of the ABP model and the quartic map of the APP model demonstrates that the amplification of speed heterogeneity depends strongly on the underlying dynamical mechanism and directly shapes the resulting non-Gaussian displacement profiles. The proposed framework therefore provides a statistically validated and physically interpretable link between experimentally observed motility variability and macroscopic transport behavior.