Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the laplace distribution calculator works
f(x)=exp(−|x−μ|/b)/(2b), with location μ and scale b>0.
Laplace data are symmetric around the location but place more probability near the center and in the tails than a normal model.
Worked example
Laplace Distribution example
For location 0 and scale 1, the cumulative probability at x=0 is 0.5 and the density is 0.5.
f(x)=exp(−|x−μ|/b)/(2b), with location μ and scale b>0.
Supported inputs
Precision and limits
Model and design
Scale b is not the standard deviation; the standard deviation is √2 b, and suitability must be checked against the process or data.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Laplace data are symmetric around the location but place more probability near the center and in the tails than a normal model.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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