Choose a tool
Pick a sampler, diagnose randomness, or explore stochastic processes.
Samplers
Generate samples from common distributions and export results.
Open Dirichlet distribution generator
Open Truncated normal generator
Open Beta distribution generator
Diagnostics & randomness
Check bias, visualize null distributions, and review randomness quickly.
Stochastic processes
Simulate random walks and Markov chains to see distributions evolve.
Quick start
- 1) Need samples? Start with Distribution sampler for common distributions.
- 2) Checking randomness? Use Randomness tests or Shuffle bias comparison.
- 3) Exploring processes? Visualize random walks and Markov chains.
Use small sample sizes first so you can verify settings quickly.
After that, increase the sample size and compare shape stability.
When you need reproducible runs, use a fixed seed and save the share URL.
Keep notes on mode, seed, and sample size for each run.
Seeded mode or secure mode?
Seeded mode is best for lessons, documentation, and debugging because you can replay the same sequence.
Secure mode is best for fairness-sensitive draws because it uses system randomness.
Pick one mode, record it, and keep it consistent across your comparison runs.
Start small. Check shape. Increase size. Recheck shape. Then export.
Guides & next steps
Explore probability and simulation topics, or return to the full Random tools hub.
How to use this tool effectively
This guide helps you use Random distributions in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.
How it works
The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.
When to use
Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.
Common mistakes to avoid
- Changing multiple parameters at once, which hides the true cause of output movement.
- Mixing units (percent vs decimal, monthly vs yearly, gross vs net) across scenarios.
- Comparing with another tool without aligning defaults, constants, and rounding rules.
- Using rounded display values as exact downstream inputs without re-checking precision.
Interpretation and worked example
Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.
See also
FAQ
What should I do first on this page?
Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.
Why does this page differ from another tool?
Different pages often use different defaults, units, rounding rules, or assumptions. Align those settings before comparing outputs. If differences remain, compare each intermediate step rather than only the final number.
How reliable are the displayed values?
Values are computed in the browser and rounded for display. They are good for planning and educational checks, but for regulated or high-stakes decisions you should validate assumptions with official guidance or professional review.
Can I share and reproduce this result?
Yes. Use the share or URL controls when available. Keep a baseline case and one changed case so others can reproduce your reasoning and verify that the direction and scale of change are consistent.
Is my input uploaded somewhere?
Core calculations run locally in your browser. Some pages encode parameters in a shareable URL, but no automatic upload is performed unless you explicitly share that link.
How to use Random distributions effectively
How this tool helps
Tools are designed for quick scenario comparisons. They work best when you keep one question per run, define success criteria first, and avoid switching objectives mid-stream. This reduces decision noise and produces results you can defend in follow-up review.
Input validation checklist
Before running, verify that required values are in the right format, that optional flags are intentionally set, and that baseline assumptions reflect current conditions. Invalid assumptions are often mistaken for tool bugs, so validation is part of interpretation quality.
Scenario planning pattern
Build three rows: conservative, expected, and aggressive cases. Keep data sources transparent for each case and compare output spacing. The pattern helps you spot non-linear jumps and decide whether a model is stable under plausible variation.
When to revisit inputs
Revisit inputs when input scale changes, time window shifts, or downstream decisions add new constraints. If constraints change, your previous output remains a useful reference but should not be treated as final guidance.
Operational checkpoint 1
Record the exact values and intent before you finalize any comparison. Confirm the unit system, date context, and business constraints. Compare outputs side by side and check whether differences are explained by one changed variable or by hidden assumptions. This checkpoint often reveals the single factor that changed everything.
How to use Random distributions effectively
How this tool helps
Tools are designed for quick scenario comparisons. They work best when you keep one question per run, define success criteria first, and avoid switching objectives mid-stream. This reduces decision noise and produces results you can defend in follow-up review.
Input validation checklist
Before running, verify that required values are in the right format, that optional flags are intentionally set, and that baseline assumptions reflect current conditions. Invalid assumptions are often mistaken for tool bugs, so validation is part of interpretation quality.
Scenario planning pattern
Build three rows: conservative, expected, and aggressive cases. Keep data sources transparent for each case and compare output spacing. The pattern helps you spot non-linear jumps and decide whether a model is stable under plausible variation.
When to revisit inputs
Revisit inputs when input scale changes, time window shifts, or downstream decisions add new constraints. If constraints change, your previous output remains a useful reference but should not be treated as final guidance.