T.01 / DISTRIBUTION TABLES
Interactive Distribution Tables — Numbers Meet Curves
Those tables in the back of your textbook — rows of tiny numbers with no visual anchor. Click a cell and its position on the distribution curve is highlighted instantly. All values computed in real time → How it works
How This Table Works
These values are not hardcoded. Two mechanisms are at work:
- Initial render — The moment you open this page, JavaScript calls mathematical functions in your browser to compute every cell from scratch. The same numbers you'd find in a printed table are being derived right here in your browser.
- Live recalculation — When you switch modes (CDF / upper / two-sided) or change parameters via sliders, the math functions are called again and every cell is instantly rewritten. This is impossible with a static table.
Methods & Precision
| Distribution | Method | Precision |
|---|---|---|
| Normal | Polynomial approximation of erf Abramowitz & Stegun (1964), formula 7.1.26. A 5-term polynomial approximates erf, then normCDF(z) = 0.5 × (1 + erf(z/√2)) |
Max error ~1.5×10⁻⁷ All 4 displayed digits (0.xxxx) match published tables exactly |
| t | Numerical integration of the PDF + bisection tPDF is integrated from −30 to x via Simpson's rule (500 intervals) to obtain the CDF. Critical values are found by bisection on the CDF (60 iterations, precision ~10⁻¹⁸) |
3 displayed digits: reliable At very low df (1–2), the integration step size (~0.07) may cause ±1 in the last digit |
| Chi-square | Regularized incomplete gamma + bisection P(χ²≤x) is expressed via the incomplete gamma function P(a,x). Series expansion below a+1, continued fraction (Lentz's method) above, up to 200 terms. Critical values by bisection (60 iterations) |
Convergence threshold 10⁻¹⁰ 3 displayed digits match published tables |
| F | Regularized incomplete beta + bisection The F-distribution CDF is converted to the incomplete beta function I_x(a,b), evaluated via continued fraction (Lentz's method, up to 200 terms). Critical values by bisection (60 iterations) |
Convergence threshold 10⁻¹⁰ 2–3 displayed digits match published tables |