Generate realistic samples from major distributions with clear controls. Review statistics, histograms, and exports quickly. Test assumptions with repeatable simulations and practical summaries today.
| Distribution | Key Inputs | Example Mean | Example Variance | Typical Use |
|---|---|---|---|---|
| Normal | μ = 0, σ = 1 | 0.0000 | 1.0000 | Measurement noise |
| Uniform | a = 2, b = 8 | 5.0000 | 3.0000 | Equal-range uncertainty |
| Binomial | n = 12, p = 0.40 | 4.8000 | 2.8800 | Success counts |
| Poisson | λ = 5 | 5.0000 | 5.0000 | Arrival counts |
Core sampling idea: Generate many random draws from a chosen distribution, then summarize the simulated sample using descriptive statistics.
Sample mean: x̄ = (Σxᵢ) / n
Sample variance: s2 = Σ(xᵢ - x̄)2 / (n - 1)
Standard deviation: s = √s2
Percentiles: Interpolated from the sorted sample.
Supported formulas: Uniform, Normal, Bernoulli, Binomial, Poisson, Exponential, and Geometric moments are included.
After you run the form, this panel shows formulas for the active distribution.
Choose a distribution first. Enter its parameters, select a sample size, and optionally set a seed for repeatable results.
Press Run Simulation. The results section appears above the form, followed by the Plotly chart and a preview of generated values.
Compare simulated and theoretical moments to judge sampling error. Then export the generated values as CSV or download the summary as PDF.
It generates many sample values from a selected probability distribution, then reports descriptive statistics, percentiles, support, and a visual graph.
Yes. Enter the same seed value to reproduce identical samples, summary statistics, and charts for the same distribution and parameters.
The simulator uses pseudo-random numbers, which are appropriate for education, testing, and many modeling tasks. Cryptographic use needs dedicated secure generators.
Continuous distributions display histograms because exact repeats are rare. Discrete distributions use frequency bars so probabilities remain easy to compare.
The theoretical mean and variance come from distribution formulas. Simulated values come from generated samples, so they move slightly as sample size changes.
Larger sample sizes usually make simulated statistics closer to theoretical values. They also produce smoother charts, but increase processing and memory usage.
This version supports Uniform, Normal, Bernoulli, Binomial, Poisson, Exponential, and Geometric models. These cover many common discrete and continuous scenarios.
Use CSV when you need raw simulated values for spreadsheets or analysis. Use PDF when you want a portable summary for reporting or sharing.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.