Negative Binomial Calculator
Find the probability of observing a number of failures before a target number of successes.
Negative Binomial Formula
P(K=k)=C(k+r−1,k)(1−p)^k p^r. This distribution models repeated independent trials until a specified number of successes occurs.
How the Negative Binomial Distribution Works
The negative binomial distribution models how many failures occur before a specified number of successes in repeated independent trials with constant success probability.
Negative Binomial Example
If success probability is 0.4 and you want the third success, the calculator can estimate the probability of observing a chosen number of failures first.
Practical Use
This distribution extends the geometric model from the first success to the r-th success and is useful for repeated-trial count problems.
Frequently Asked Questions
Is geometric a special case?
Yes, when the target number of successes is one.
Must trials be independent?
Yes for the standard model.
Can success probability change?
Not in the basic negative binomial model.
Methodology, Assumptions and Interpretation
A negative-binomial model describes the number of trials or failures needed to reach a specified number of successes under independent trials with constant success probability. Parameter conventions vary, so confirm what the calculator counts.