{ "category": "Compatibility", "display_name": "WEIBULL", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.WEIBULL", "implementation_state": { "answer_bank": null, "detail": "Recorded: 6 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 6 recorded answers", "workbook_corpus": { "cells": 6, "matched": 6 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L248-L251", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/special_dist_family.rs#L224-L231" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/distributions::nums", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_expm1_internal", "ported/excel_numeric::expm1_internal_graph", "ported/excel_numeric::excel_pow_chain", "ported/excel_numeric::excel_x87_sub", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_x87_div", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87::sub", "ported/excel_numeric/x87::div", "ported/excel_numeric/x87_chains::pow2_positive", "ported/excel_numeric/x87_chains::pow2", "ported/excel_numeric/x87_chains::exp_ext", "ported/excel_numeric/x87_chains::exp_with", "ported/excel_numeric/x87_chains::excel_exp", "ported/excel_numeric/x87_chains::log_with", "ported/excel_numeric/x87_chains::excel_log", "ported/special_dist_family::weibull_dist_kernel" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L248-L251", "state": "matches", "suite": null, "summary": "Matches all 6 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.WEIBULL.json", "name": "WEIBULL", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[WEIBULL.DIST](FUNC.WEIBULL.DIST.md) is the modern spelling; [EXPON.DIST](FUNC.EXPON.DIST.md) is the shape-one special family; [GAMMA.DIST](FUNC.GAMMA.DIST.md) supplies another positive-valued distribution.\n\n\n", "how-to-implement": "\nFor positive inputs, define a raw power helper `P(a,b)=EXP(R(b*LN(a)))`, using the public stored LN and EXP leaves and the [stored operation R](../model/09-staged-arithmetic.md). The current route uses this chain even for integer exponents and square roots; a host `pow` shortcut changes the candidate.\n\n1. Validate finite inputs and the documented sign domain; handle the code’s zero-input branch separately.\n2. Store `r=R(x/beta)`, then obtain `t=P(r,alpha)`.\n3. For the CDF, compute `-expm1_internal(-t)`. Here the Kahan correction uses ordinary binary64 arithmetic: with `u=EXP(-t)`, return `t` if `u==1`; otherwise return `-(u-1)` for `t>=1`, or `-((u-1)*(-t)/LN(u))` for `t<1`.\n4. For density, obtain `B=P(beta,alpha)`, `X=P(x,alpha-1)` and `E=EXP(-t)`. Evaluate division first and multiply left to right: `R(R(R(alpha/B)*X)*E)`.\n5. The helper rejects a nonfinite result with `#NUM!`. Keep worksheet publication separate from the polynomial/power body.\n\nFor `x=4,alpha=2,beta=2`, the mathematical reduction has `r=2`, `t=4`, `alpha/beta^alpha=0.5`, and `x^(alpha-1)=4`; density is therefore `2*exp(-4)`. The raw power chain need not publish exact integer four at each intermediate stage, so the mathematical trace is not permission to remove those calls.\n\nThe cited source retains positive-input power-staging discriminants, including 113 controls separating the stored exponent product. Exact global branch boundaries and a whole-domain legacy-spelling result remain unestablished here. No Handbook suite is published for this function.\n\n\n", "quirks": "\nNegative `x` or a nonpositive shape or scale gives `#NUM!`; nonnumeric numeric arguments give `#VALUE!`. Densities and cumulative probabilities are different quantities, even when they happen to have similar decimal values.\n\nAt zero, the mathematical CDF is zero. The density’s right-hand limit is zero for `alpha>1`, `1/beta` for `alpha=1`, and unbounded for `0