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 inverse gaussian distribution calculator works
f(x)=√[λ/(2πx³)] exp{−λ(x−μ)²/(2μ²x)}, x>0.
The mean parameter sets location on the positive scale while larger shape concentrates observations more tightly around it.
Worked example
Inverse Gaussian Distribution example
With mean μ=1 and shape λ=1, the density at x=1 is 1/√(2π)≈0.398942.
f(x)=√[λ/(2πx³)] exp{−λ(x−μ)²/(2μ²x)}, x>0.
Supported inputs
Precision and limits
Model and design
This mean-shape parameterization differs from some software scale conventions; process fit and first-passage assumptions require separate review.
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
The mean parameter sets location on the positive scale while larger shape concentrates observations more tightly around it.
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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