Negative Hypergeometric Distribution
Draw without replacement until a chosen marked item arrives and inspect the exact waiting-time distribution.
Free theory articleDraw without replacement until a chosen marked item arrives and inspect the exact waiting-time distribution.
Concept & interpretation
Choose a finite bag of N items with K marked, and define T as the total draw index of the rth marked item without replacement. The negative hypergeometric distribution describes the exact waiting-time distribution.
Experiment
Using the Negative Hypergeometric Distribution module, we can explore how the parameters affect the waiting time.
- Select the bag preset "10 with4 marked".
- Set the marked target r to 2.
- Observe the exact mean is 4.4, variance is 2.64, and feasible support is 2 to 8.
- Probe the draw t = 5 to see the exact probability is 4/21.
Notice that if you set K < r (e.g., target 1 in "No marked"), the module reports the target is impossible.