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Probability Distribution Explorer

Understand distributions visually. Adjust parameters, measure probabilities, compare curves, and simulate outcomes — entirely in your browser.

Private calculations · No uploads

Normal distribution

Probability density and selected region

Current distribution
Probability distribution chartAdjust parameters and select a probability query to update the chart. Accessible numeric results appear below.

The filled area represents the selected probability. The vertical axis is probability density, not probability, for continuous distributions.

Probability calculator

Select a region or solve for a percentile.

02
Probability query
Central interval
P(−1 ≤ X ≤ 1)68.27%
Decimal0.68269

Continuous intervals include their endpoints; endpoints have zero probability individually.

Presets use equal-tail quantiles; for discrete outcomes, actual coverage may exceed the selected target.

x = 1.645

Reproducible simulation

Generate data from the selected distribution using a deterministic seed.

03
No simulated data generated.
Ready. All calculations run locally in this browser.

Understand probability distributions

Continuous versus discrete

Normal, gamma, beta and exponential models use a density function (PDF). Probabilities are areas under a curve. Binomial, Poisson and geometric models use a probability mass function (PMF) for individual integer outcomes.

Which distribution should I use?

Use normal for approximately symmetric measurements; binomial for successes in fixed independent trials; Poisson for counts at a rate; exponential for waiting time; and Student’s t when modeling heavy-tailed sampling variation.

Percentiles, tails, and precision

The cumulative distribution function (CDF) returns P(X ≤ x). A percentile finds the smallest value with at least the requested cumulative probability. Discrete percentiles step between integers, unlike smooth continuous quantiles.

This is an educational probability calculator, not a hypothesis-testing or financial risk certification tool. Extremely small tail probabilities can be limited by floating-point precision. Sample generation is deterministic for exploration, not cryptographically secure.

Using Probability Distribution Explorer

Explore supported probability distributions with PDF/PMF, CDF, interval and tail queries, seeded samples, and exportable charts or tables.

Workflow

  1. Choose a supported distribution and enter valid parameters
  2. review density or mass, cumulative probability and interval queries
  3. generate a seeded sample if needed and export plots, CSV or settings.

Example

Choose a normal distribution with a fixed mean and spread, compare a central interval with a tail query, then generate a seeded sample and export the chart and summary.

Limits and data handling

These are bounded double-precision calculations, not fitted models or statistical guarantees. Discrete outside queries exclude endpoints. Equal-tail intervals may differ from target mass, and histogram bins restricted to the observed sample range can omit out-of-range sample values. Parameter changes invalidate old simulations. Check the selected distribution and assumptions before interpreting results.

FAQs

Does a probability curve show that data fits the distribution?

No. The explorer calculates a selected theoretical distribution; it does not fit or validate a model against your data.

Does a seeded sample guarantee statistical accuracy?

No. A seed makes the generated sequence repeatable, not representative or statistically guaranteed.

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