Distribution Generator & Visualizer

About the Distribution Generator & Visualizer

Probability distributions are easier to understand when you can see them. This tool draws thousands of random numbers from the distribution you choose and plots them as a histogram, then overlays the exact theoretical curve: the probability density function (PDF) for continuous distributions, or the probability mass function (PMF) for discrete ones. Slide the parameters and the shape changes in real time, so you can build intuition for how each distribution behaves.

Everything runs in your browser using a built-in statistics engine, so it's instant and private: great for students, teachers, data scientists, and anyone curious about how randomness is shaped.

Distributions included

• Continuous: Normal (Gaussian), Uniform, Exponential, Log-normal, Gamma, Beta, Chi-squared, Student's t, Cauchy, Laplace, Logistic, Weibull, Pareto, Rayleigh, Gumbel, Triangular, F, Maxwell–Boltzmann, and Half-normal.
• Discrete: Bernoulli, Binomial, Poisson, Geometric, Negative binomial, Discrete uniform, and Hypergeometric.

What you can do

• Adjust parameters live: every distribution has the right knobs (mean, rate, shape, scale, etc.) with sliders and exact value boxes. Typed values outside the valid domain are coerced (a negative sigma snaps back, a uniform with a > b swaps).
• Three views: the histogram with its exact PDF/PMF overlay, a CDF view comparing the empirical CDF to the exact theoretical one, and a Q-Q plot of sample quantiles against exact theoretical quantiles.
• Compare sample to theory: a moments table shows sample mean, standard deviation, skewness, and excess kurtosis next to their closed-form values, and marks moments that do not exist (try the Cauchy).
• Reproduce a draw: set a seed and every resample returns the identical sample; the CSV and PNG filenames record it.
• Take the code with you: R and Python (numpy + scipy) snippets update live with your parameters, using each library's actual parameterization.
• Export: download the sample as CSV, copy it to the clipboard, or save an annotated PNG of the current view.

Good to know

• The histogram is normalized to a density (or probability) so it lines up with the theoretical curve, and you can override the automatic bin count.
• CDFs are computed exactly via the error function, the regularized incomplete gamma function, and the regularized incomplete beta function, not by simulation.
• Q-Q quantiles come from inverting the exact CDF; the extreme 0.5% tails are trimmed so heavy-tailed distributions stay readable.
• Heavy-tailed distributions (like Cauchy and Pareto) are plotted over their central range so the shape stays readable.
• Sampling uses standard methods (Box-Muller for normals, Marsaglia-Tsang for the gamma family, which powers beta, chi-squared, t, and F), driven by a seedable mulberry32 generator.

Common questions

What does a normal distribution look like versus exponential or Poisson?

Pick each one and see: the normal's symmetric bell, the exponential's steep decay, the Poisson's discrete counts. Watching samples pile into each shape builds the intuition that formulas alone never quite deliver.

How do distribution parameters change the shape?

Adjust them live and watch: widen a normal's sigma and the bell flattens, raise a gamma's shape parameter and the skew relaxes. The immediate feedback is the fastest way to learn what each parameter really controls.

Which distribution should I use to model my data?

Match the story: normal for sums of many small effects, exponential for waiting times, Poisson for counts of rare events, Weibull for failure times, Pareto for heavy-tailed sizes. Generate each candidate here and compare its shape against your data's histogram.

Can I generate random sample data for testing?

Yes. Set the distribution and parameters that match realistic behavior (latencies, arrivals, purchase amounts) and sample as many values as your load test or seed script needs.

Is this useful for statistics courses?

That is half its job: 26 distributions with live parameters make it a visual companion for probability and stats classes, and the sampling view connects the theoretical curve to what real data from it looks like.

Can I get R or Python code for a probability distribution?

Yes. Every distribution shows ready-to-run R and Python (numpy plus scipy) snippets with your current parameter values filled in, using the correct parameterization for each library, including the traps: numpy's pareto is actually Lomax, R's rgeom counts failures rather than trials, and scipy's lognormal takes the log-sd as its shape parameter.

How do I check whether data follows a given distribution?

Use the Q-Q plot view: it plots sample quantiles against exact theoretical quantiles, so points hugging the 45-degree line mean a good fit and curved tails reveal skew or heavy tails. The CDF view and the sample-versus-theory moments table give two more angles on the same question.

Related tools