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Statistics · Distributions

Inverse Gaussian Distribution Calculator

Evaluate density, tails, quantiles, and moments for a positive inverse Gaussian first-passage model using mean and shape.

Statistics · Distributions

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Private in-browser calculation · explicit assumptions
Continuous support is shown as a scale. Probability belongs to area over an interval, not to the density height at one point.
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  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

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Understand the distribution

What the inverse gaussian distribution calculator models

Modeling positive waiting times or lifetimes. Positive-support families offer different hazard and shape behavior. Parameter names and rate-versus-scale conventions must match the formula being used.

Density and cumulative rule

f(x)=√[λ/(2πx³)] exp{−λ(x−μ)²/(2μ²x)}, x>0.

A density height is not itself a probability. Continuous probability is the area accumulated across an interval.

Interpretation and limits

The mean parameter sets location on the positive scale while larger shape concentrates observations more tightly around it.

Model boundary: This mean-shape parameterization differs from some software scale conventions; process fit and first-passage assumptions require separate review.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. 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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