Geometric Distribution Calculator
Calculate geometric distribution using your data.
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What this tool does
Calculate geometric distribution using your data. Trials are independent with constant success probability. This is the trials-until-first-success (support 1, 2, 3, …) form of the geometric distribution.
How to use the Geometric Distribution Calculator
- Enter or select success probability per trial (%).
- Enter or select trial of first success (k).
- Read the calculated result; change any measurement to compare alternatives.
Formula
P(first success on trial k) = (1−p)^(k−1) p; P(X ≤ k) = 1 − (1−p)^k; mean trials = 1/p
- pp
- Success probability per trial (%)
- kk
- Trial of first success (k)
Trials are independent with constant success probability. This is the trials-until-first-success (support 1, 2, 3, …) form of the geometric distribution.
Worked example
For geometric distribution calculator, the following measurements illustrate the exact method: Success probability per trial (%): 20; Trial of first success (k): 3.
Inputs
- Success probability per trial (%)20
- Trial of first success (k)3
Result
- P(first success exactly on trial k) (%)12.8
- P(first success within k trials) (%)48.8
- Expected trials to first success5
Results explained
- P(first success exactly on trial k) (%)
- P(first success exactly on trial k) (%) from the formula above. Trials are independent with constant success probability. This is the trials-until-first-success (support 1, 2, 3, …) form of the geometric distribution.
- P(first success within k trials) (%)
- P(first success within k trials) (%) from the formula above. Trials are independent with constant success probability. This is the trials-until-first-success (support 1, 2, 3, …) form of the geometric distribution.
- Expected trials to first success
- Expected trials to first success from the formula above. Trials are independent with constant success probability. This is the trials-until-first-success (support 1, 2, 3, …) form of the geometric distribution.
Frequently asked questions
P(first success on trial k) = (1−p)^(k−1) p; P(X ≤ k) = 1 − (1−p)^k; mean trials = 1/p
Trials are independent with constant success probability. This is the trials-until-first-success (support 1, 2, 3, …) form of the geometric distribution.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.