Accurate simulation sampling for Mittag–Leffler waiting-time distributions

Develop a precise simulation-sampling method for Mittag–Leffler-type power-law waiting-time distributions in continuous-time random-walk diffusion models, avoiding the bias produced by replacing them with standard Pareto-type distributions.

Background

The paper analyzes intermittent continuous-time random walks under a renewal reset mechanism and considers power-law waiting-time distributions represented by Mittag–Leffler functions. Although analytical results are derived for stationary states, mean-square displacements, and first-arrival times, the authors do not provide simulations for Mittag–Leffler waiting times.

The stated difficulty is numerical rather than analytical: the commonly used replacement of Mittag–Leffler waiting-time distributions by standard Pareto-type distributions is reported to produce systematically biased simulation results, even when graphical comparisons on log–log plots appear close. Developing an unbiased and accurate sampling procedure would enable reliable numerical validation of the model for power-law waiting times.