Math calculator
Negative Binomial Distribution Calculator
Find the chance the rth success occurs on trial k. The page traces how the inputs become final-success probability before rounding.
Negative Binomial Distribution inputs
Enter the source values
An independent route for Negative Binomial Distribution
For a small Negative Binomial Distribution example using Required successes r, Trial of rth success k, Success probability p, solve once with the displayed formula and once through direct enumeration or a probability tree. Two methods that organize outcomes differently are less likely to share the same hidden assumption error.
For Negative Binomial Distribution, when the exact list becomes too large, retain a simpler identity as a check: complementary probabilities sum to one, a Pascal row is symmetric, and adjacent factorial results have a known ratio. State which identity was used beside the reported answer.
Reviewing the Negative Binomial Distribution case
Preserve Required successes r when checking the Negative Binomial Distribution output. Keep Trial of rth success k under the same convention and estimate Final-success probability. A controlled change to Success probability p should move the Negative Binomial Distribution Final-success probability in a mathematically consistent direction.
A final Negative Binomial Distribution check
The displayed Final-success probability belongs to this Negative Binomial Distribution setup; altered inputs should be saved as a separate calculation case.
Reviewing Negative Binomial Distribution in context
The negative-binomial and binomial models differ in which event count is held fixed. For that connected step, see binomial model.
Try a boundary value relevant to Required successes r while holding Trial of rth success k constant. The resulting Negative Binomial Distribution case can reveal a hidden limit or branch.
Preserve the units and conventions attached to Required successes r. They determine how Final-success probability should be interpreted in this Negative Binomial Distribution problem.
Substitute Final-success probability into the defining Negative Binomial Distribution relation when reversal is possible. A mismatch points back to Required successes r, Trial of rth success k, or a convention.
Change only Required successes r during a Negative Binomial Distribution trial. With Trial of rth success k unchanged, the movement in Final-success probability should follow the stated mathematical relationship.
Questions about Negative Binomial Distribution
What if r=1?
The result is geometric.
Why choose from k−1?
The kth trial is fixed as success.
Can k<r?
No.
What stays constant?
The per-trial probability.