{ "category": "Statistical functions", "display_name": "BETA.INV", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.BETA.INV", "implementation_state": { "answer_bank": null, "detail": "Everything else matches (6 workbook cells). Last-bit means a finite number within 16 ULP of Excel's.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "close", "state_label": "Close: last-bit deviations remain", "summary": "Close: 1 of 6 recorded answers differ in the last bits, worst 2 ULP", "workbook_corpus": { "cells": 6, "last_bit": 1, "matched": 5, "worst_ulp": 2 } }, "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#L211-L216" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/distributions::nums", "ported/beta_gamma_stats_family::validate_beta_shape", "ported/beta_gamma_stats_family::beta_inv_kernel", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_x87_add", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_x87_mul_add", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87::add", "ported/special_math_common::bratio_ftoi", "ported/special_math_common::bratio_spmpar1", "ported/special_math_common::bratio_exparg", "ported/special_math_common::bratio_esum", "ported/special_math_common::bratio_esum20", "ported/special_math_common::bratio_alnrel", "ported/special_math_common::bratio_rlog1", "ported/special_math_common::bratio_gam1", "ported/special_math_common::bratio_gamln1", "ported/special_math_common::bratio_gamln", "ported/special_math_common::bratio_algdiv", "ported/special_math_common::bratio_bcorr", "ported/special_math_common::bratio_gsumln", "ported/special_math_common::bratio_betaln", "ported/special_math_common::bratio_betaln_60", "ported/special_math_common::bratio_erf_nswc", "ported/special_math_common::bratio_erfc1", "ported/special_math_common::bratio_rexp", "ported/special_math_common::bratio_psi", "ported/special_math_common::bratio_fpser", "ported/special_math_common::bratio_apser", "ported/special_math_common::bratio_bpser", "ported/special_math_common::bratio_bup", "ported/special_math_common::bratio_brcomp", "ported/special_math_common::bratio_brcmp1", "ported/special_math_common::bratio_bfrac", "ported/special_math_common::bratio_bgrat", "ported/special_math_common::bratio_grat1", "ported/special_math_common::bratio_basym", "ported/special_math_common::bratio", "ported/special_math_common::regularized_beta", "ported/special_math_common::bisect_inverse" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L211-L216", "state": "close", "suite": null, "summary": "Close: 1 of 6 recorded answers differ in the last bits, worst 2 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.BETA.INV.json", "name": "BETA.INV", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[BETA.DIST](FUNC.BETA.DIST.md) evaluates the forward CDF or density. [BETAINV](FUNC.BETAINV.md) is the compatibility spelling. [F.INV](FUNC.F.INV.md) and [T.INV](FUNC.T.INV.md) use related beta-ratio mathematics with distinct wrappers.\n\n\n", "how-to-implement": "\n1. Apply optional bounds and validate finite positive shapes, finite ordered bounds and probability under the chosen endpoint contract.\n2. Use the current regularized lower beta callback F(z), including its stored complement `1-z` and internal beta-ratio approximation.\n3. Search z between zero and one by bisecting the ordered nonnegative binary64 encodings. At each midpoint, keep the upper half when F(z) is below p and the lower half otherwise. Return the upper endpoint once adjacent, as in [BETAINV’s detailed search recipe](FUNC.BETAINV.md#how-to-implement).\n4. Store `width=B-A`, `scaled=z*width` and `result=A+scaled` with ordinary binary64 arithmetic and separate multiplication/addition. Apply the worksheet’s numeric publication rule.\n\nIn the first example, z is about one half and the last three stages give width four, scaled two and result four. An arithmetic-midpoint search, a residual tolerance, an FMA or an explicit endpoint shortcut can change stored results and boundary behaviour.\n\nAt p=0 the usual strict lower-bracket invariant already fails at z=0. The current search can select the smallest positive binary64 value rather than exactly zero. A mathematical inverse can handle that endpoint explicitly; reproducing this code instead requires retaining its search and publication stages.\n\nInverse accuracy depends on the forward surface being searched. A round trip through that same surface can hide a shared error. The beta approximation, extreme affine scaling and remaining inverse mismatches are still open; there is no published whole-function Handbook suite.\n\n\n", "quirks": "\nMicrosoft documents `#VALUE!` for nonnumeric arguments and `#NUM!` for nonpositive shapes or probability at/below zero or above one. The current implementation also rejects unordered bounds.\n\nThe current helper’s validation admits zero probability but has no zero-endpoint shortcut before searching adjacent binary64 values. On the standard interval this can leave a subnormal value that its publisher refuses; on two to six the affine addition rounds it to two. This code-path behaviour is not a measurement of Excel’s endpoint.\n\nThe legacy BETAINV shares the current helper. Shared code does not establish that all Excel builds compute the two names identically.\n\n\n", "sources": "\n- [Microsoft: BETA.INV function](https://support.microsoft.com/en-us/excel/functions/beta-inv-function), opened 7 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/beta_gamma_stats_family.rs); implementation steps and the limits identified in the text.\n- [Beta callback and ordered-value inverse](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/special_math_common.rs); `regularized_beta` and `bisect_inverse`.\n\n", "try-it": "\n`=BETA.INV(0.25,2,1,2,6)` is about `4`. On the standard interval, these shapes give CDF `z^2`; probability one quarter therefore selects z one half. Rescaling gives `2+0.5*4=4`.\n\n`=BETA.INV(0.25,1,1,2,6)` is about `3`: the uniform shape-one case has CDF z itself.\n\n\n", "version-differences": "\nNo same-input comparison between named Excel builds is recorded for this function here. The documented behaviour below is not a measurement of every Excel release.\n\n\n", "what-it-does": "\n`BETA.INV(probability,alpha,beta,[A],[B])` returns the value whose beta CDF is the requested probability. Shapes alpha and beta are positive. Bounds default to zero and one; supplying other bounds rescales the value interval, while probability remains on zero to one.\n\n\n" }, "signature": { "display": "BETA.INV(probability, alpha, beta, [A], [B])", "parameters": [ { "description": null, "name": "probability", "optional": false, "repeats": false }, { "description": null, "name": "alpha", "optional": false, "repeats": false }, { "description": null, "name": "beta", "optional": false, "repeats": false }, { "description": null, "name": "A", "optional": true, "repeats": false }, { "description": null, "name": "B", "optional": true, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 5, "min": 3 }, "category": "Statistical functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "None", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "The value at which the cumulative beta distribution reaches a given probability", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the inverse of the cumulative distribution function for a specified beta distribution", "microsoft_url": "https://support.microsoft.com/en-us/office/beta-inv-function-e84cb8aa-8df0-4cf6-9892-83a341d252eb" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "BETA.INVn" }, { "locale": "bg-BG", "name": "BETA.INVn" }, { "locale": "cs-CZ", "name": "BETA.INVn" }, { "locale": "da-DK", "name": "BETA.INVn" }, { "locale": "de-DE", "name": "BETA.INVn" }, { "locale": "el-GR", "name": "BETA.INVn" }, { "locale": "en-AU", "name": "BETA.INVn" }, { "locale": "en-GB", "name": "BETA.INVn" }, { "locale": "en-US", "name": "BETA.INVn" }, { "locale": "es-ES", "name": "BETA.INVn" }, { "locale": "et-EE", "name": "BETA.INVn" }, { "locale": "fi-FI", "name": "BEETA. KÄÄNT" }, { "locale": "fr-FR", "name": "BETA.INVn" }, { "locale": "he-IL", "name": "BETA.INVn" }, { "locale": "hr-HR", "name": "BETA.INVn" }, { "locale": "hu-HU", "name": "INVERZ.BÉTA" }, { "locale": "id-ID", "name": "BETA.INVn" }, { "locale": "it-IT", "name": "BETA.INVn" }, { "locale": "ja-JP", "name": "BETA.INVn" }, { "locale": "ko-KR", "name": "BETA.INVn" }, { "locale": "lt-LT", "name": "BETA.INVn" }, { "locale": "lv-LV", "name": "BETA.INVn" }, { "locale": "nb-NO", "name": "BETA.INVn" }, { "locale": "nl-NL", "name": "BETA.INVn" }, { "locale": "pl-PL", "name": "BETA.INVn" }, { "locale": "pt-BR", "name": "BETA. INVn" }, { "locale": "pt-PT", "name": "BETA. INVN" }, { "locale": "ro-RO", "name": "BETA.INVn" }, { "locale": "ru-RU", "name": "BETA.INVn" }, { "locale": "sk-SK", "name": "BETA.INVn" }, { "locale": "sl-SI", "name": "BETA.INVn" }, { "locale": "sr-Latn-RS", "name": "BETA.INVn" }, { "locale": "sv-SE", "name": "BETA.INVn" }, { "locale": "th-TH", "name": "BETA.INVn" }, { "locale": "tr-TR", "name": "BETA.INVn" }, { "locale": "uk-UA", "name": "BETA.INVn" }, { "locale": "vi-VN", "name": "BETA.INVn" }, { "locale": "zh-CN", "name": "BETA.INVn" }, { "locale": "zh-HK", "name": "BETA.INVn" }, { "locale": "zh-TW", "name": "BETA.INVn" } ], "signature": { "display": "BETA.INV(probability, alpha, beta, [A], [B])", "parameters": [ { "description": null, "name": "probability", "optional": false, "repeats": false }, { "description": null, "name": "alpha", "optional": false, "repeats": false }, { "description": null, "name": "beta", "optional": false, "repeats": false }, { "description": null, "name": "A", "optional": true, "repeats": false }, { "description": null, "name": "B", "optional": true, "repeats": false } ], "trailing_repeats": false }, "surface_name": "BETA.INV", "version_marker": null, "xlcall": { "code": "526", "symbol": "xlfBeta_inv" } }, "microsoft": "https://support.microsoft.com/en-us/office/beta-inv-function-e84cb8aa-8df0-4cf6-9892-83a341d252eb" }, "try_it": { "formula": "=BETA.INV(0.25,2,1,2,6)" }, "url": "https://handbook.dnacalc.com/functions/BETA.INV.html", "variants": [], "versions": [] }