How are the CDFs and quantiles computed?

Binomial CDFs map to the regularized incomplete beta, Poisson and chi-square use regularized gamma functions, and Student’s t relies on a beta transform with Newton or bisection refinements for inversion.

What can I do with the exact Clopper–Pearson and Poisson intervals?

They provide rigorous confidence intervals for the binomial success rate p and the Poisson rate λ, making it easy to document uncertainty in class demonstrations or reports.

Distributions Pack Calculator — Binomial, Poisson, Student's t, Chi-square with Steps

Inputs & Modes

Distribution Mode Tail (lower / upper / two-sided)

Parameters

α (confidence level)

Result

How it’s calculated

Visualization

Discrete distributions render as bars with highlighted tails; continuous ones display the PDF curve plus shaded regions or quantile markers.

Teacher notes

The How it’s calculated log exposes every transform (beta/gamma mapping, Newton steps), making derivations easy to discuss live.
Exact intervals for binomial p and Poisson λ appear alongside point estimates so learners can compare uncertainty and probability mass.
Shareable URLs, CSV tables, and LaTeX snippets streamline homework distribution and worked-solution handouts.

FAQ

How are CDFs and quantiles computed?

Binomial CDFs use regularized incomplete beta, Poisson and chi-square rely on regularized gamma, and Student’s t maps to beta functions combined with Newton or bisection for robust inversion.

What can I do with the exact intervals?

The Clopper–Pearson interval for p and the chi-square based interval for λ quantify uncertainty exactly, so you can document precision requirements in labs or assessments.

Inputs & Modes

Result

How it’s calculated

Visualization

Teacher notes

FAQ

Related calculators