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Random Number Generator

Free random number generator. Uniform, normal, exponential, Poisson. Statistics, histogram, Q-Q plot

Run CalculatorExplore data analysis and statistical calculations

Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

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RANDOM NUMBER GENERATORStatistics

Generate from Uniform, Normal, Exponential, Poisson

Multiple distributions, optional seed, histogram, summary stats. Box-Muller for normal, inverse CDF for exponential.

Normal Distribution →Dice Probability →

Real-World Scenarios — Click to Load

Distribution

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • • PRNG vs true randomness: Computers use pseudorandom algorithms; same seed produces same sequence
  • • Uniform: each value equally likely. Normal: bell curve. Exponential: wait times. Poisson: counts
  • • Box-Muller transforms two uniforms into two normals. Inverse CDF for exponential
  • • Monte Carlo: use random numbers for simulation, integration, optimization
  • • For cryptography, use crypto.getRandomValues() or NIST-approved RNGs

Did You Know?

🎲JavaScript Math.random() is a PRNG — not cryptographically secure. Use crypto.getRandomValues() for security.Source: MDN
📐Box-Muller (1958) converts uniform [0,1] to standard normal. One of the most used transforms.Source: Wolfram
🎰Monte Carlo methods use random sampling to estimate π, integrals, and complex systems.Source: Stanford
🔐RFC 4086 recommends multiple entropy sources for security-critical randomness.Source: RFC 4086
📊Q-Q plots compare sample quantiles to theoretical — straight line means good fit.Source: NIST
⏱️Exponential distribution models wait times: P(T>t) = e^(-λt). Memoryless property.Source: Khan Academy

Expert Tips

Use seed for reproducibility

Same seed → same sequence. Essential for debugging and reproducibility.

Histogram validates distribution

Normal should look bell-shaped. Uniform flat. Exponential right-skewed.

Q-Q plot for normality

Sample vs theoretical quantiles. Straight line suggests normal fit.

Not for cryptography

Use crypto.getRandomValues() or NIST-approved RNGs for security.

Distribution Comparison

DistributionUse CaseParameters
Uniform IntDice, lottery, IDsmin, max
Uniform FloatContinuous [a,b]min, max, decimals
NormalHeights, errors, scoresΟ, σ
ExponentialWait times, lifetimesÎť (rate)
PoissonEvent counts, arrivalsÎť (mean)

Frequently Asked Questions

Is this true randomness?

No. Computers use pseudorandom number generators (PRNGs). Same seed gives same sequence. For cryptography use hardware RNGs.

What is the Box-Muller transform?

Converts two uniform [0,1] values into two standard normal values. Z = √(−2 ln U₁) cos(2π U₂).

How does exponential generation work?

X = −ln(U)/λ. This is the inverse CDF of the exponential distribution.

What is Monte Carlo?

Using random sampling to estimate quantities: π, integrals, option pricing, particle physics.

Why use a seed?

Reproducibility. Same seed → same sequence. Essential for debugging, testing, and reproducible research.

Can I use this for lottery?

Yes. Uniform integer with no duplicates. But for real lotteries, use cryptographically secure RNGs.

What is a Q-Q plot?

Compares sample quantiles to theoretical. For normal data, points should fall on a straight line.

What is entropy?

Measure of unpredictability. Cryptographic RNGs need high entropy from hardware (noise, timing).

By the Numbers

5
Distributions
PRNG
Pseudorandom
Box-Muller
Normal transform
Monte Carlo
Simulation

Disclaimer: This generator uses pseudorandom algorithms (Mulberry32 with seed, Math.random). Not suitable for cryptographic or security-critical applications. Use NIST-approved cryptographic RNGs for those purposes.

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