Inverse Gaussian First Passage
Link a positive waiting-time density to drifted Brownian first passage.
Free theory articleLink a positive waiting-time density to drifted Brownian first passage.
Concept & interpretation
The inverse Gaussian distribution, parameterized by a mean μ and a shape parameter λ, describes the time it takes for a Brownian motion with positive drift to reach a fixed positive level. It represents a waiting time, modeling first passage phenomena in physics, finance, and reliability engineering.
Experiment: Changing the shape
You can observe how the distribution shape changes by adjusting the parameters in the Inverse Gaussian First Passage module.
- Set the Mean mu to 1.
- Change the Shape lambda from 1 to 4.
- Observe that the variance decreases from 1 to 0.25, and the distribution becomes more concentrated around the mode.
- Set the Probe x to 1 and verify the density increases from 0.3989 to 0.7978.