We introduce 鈥榗umulative鈥?moments and show that moment convergence can be easily related to the distribution of the reciprocal of time-intervals (rate). The behaviour of the rate distribution near zero determines which moments in the time domain converge. Non-convergence may be very slow leading to the appearance of convergence, but after infinite time they become infinite (pseudo-convergence). Experiments take place in finite time and cannot reconcile pseudo-convergence. Nevertheless, cumulative sample moments can provide insight into the convergence of the parent moments, but this depends on sample size. We illustrate convergence issues with three empirical examples: manual reaction times, neural inter-spike intervals, and optokinetic inter-saccadic intervals. We conclude that estimating moments of skewed TI distributions is at best questionable and propose that rate (reciprocal TI) usually (but not always) provides more information.