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.

계산 방법

주요 분포의 PDF/CDF·분위수를 수치적으로 안정된 식으로 계산합니다.
입력 파라미터를 검증하고, 화면에 표시할 때만 적절히 반올림합니다.
공유 URL에 분포 종류·파라미터·모드를 함께 저장하여 동일한 결과를 다시 열 수 있습니다.