An analytic form for the interresponse time analysis of Shull, Gaynor, and Grimes with applications and extensions.

Robert and colleagues wrote new math for the old Shull-Gaynor-Grimes IRT model. They replaced computer simulations with one clean equation.

The team also added rules for two edge cases: refractory pauses and banded rapid bursts. Now the same formula covers slow, medium, and fast responding.

A closed-form equation fit the classic IRT data without Monte Carlo runs. One line of code gives the same curves that once needed hours of simulation.

The extended form predicted refractory gaps and burst bands seen in pigeon and rat records. Accuracy stayed high across all three response speeds.

Kaufman (1965) and Hart et al. (1968) showed messy IRT histograms from real animals. Robert et al. now capture those same shapes with a single equation, turning raw lab facts into a portable formula.

Hammond (1980) also swapped simulation for algebra by rewriting Herrnstein’s hyperbola. Both papers prove that hand-crank math can outperform older iterative models when you allow key parameters to move.

Parmenter (1999) argued decay models fail because they ignore scalar noise. Robert’s group side-steps that fight; their model needs no decay term, so the papers coexist rather than clash.

If you analyze response timing in the clinic or the lab, you can now fit IRT distributions in Excel without add-ins. Faster graphs mean quicker decisions about pacing, DRL, or reinforcement density. Try plugging your next session’s IRTs into the Robert equation before you write a simulation.