There is no point reaching for a calculator that cannot show its working. This one starts from n (number of events), probability of one success, r (number of successes) and one way and reports combinations (n-1, r-1) and probability of y=n, so you can see how each answer follows from the numbers you entered.
What Is the Negative Binomial Distribution Calculator?
The negative binomial distribution calculator turns a set of measurements into combinations (n-1, r-1) and probability of y=n, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the Negative Binomial Distribution Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with n (number of events) set to 10, probability of one success set to 5, r (number of successes) set to 2, the calculator returns combinations (n-1, r-1) of 9, and probability of y=n of 14,745,600. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out combinations (n-1, r-1)?
Enter n (number of events), probability of one success, r (number of successes) and one way. The calculator then works through the relationship and reports combinations (n-1, r-1) and probability of y=n.
What does the negative binomial distribution actually calculate?
It takes n (number of events), probability of one success, r (number of successes) and one way and converts them into combinations (n-1, r-1) and probability of y=n using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter n (number of events)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.