This geometric distribution calculator takes the figures you already have and applies the relationship behind geometric distribution calculations for you, giving geometric probability, expectation (mean) and standard deviation from number of failures and probability of success.
What Is the Geometric Distribution Calculator?
The geometric distribution calculator turns a set of measurements into geometric probability, expectation (mean) and standard deviation, 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 Geometric 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 number of failures set to 10, probability of success set to 5, the calculator returns geometric probability of 5,242,880, and expectation (mean) of -0.8, and variance of -0.16. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out geometric probability?
Enter number of failures and probability of success. The calculator then works through the relationship and reports geometric probability, expectation (mean) and standard deviation.
What does the geometric distribution actually calculate?
It takes number of failures and probability of success and converts them into geometric probability, expectation (mean) and standard deviation 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 number of failures?
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.
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.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.