{ "category": "Compatibility", "display_name": "BETAINV", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.BETAINV", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "?" ], "larger_numeric": 0, "last_bit": 44, "matched": 18, "other_mismatch": 0, "refused": 0, "rows": 62, "unread": 0, "worst_ulp": 12 }, "detail": "Everything else matches (62 in the answer bank and 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: 46 of 68 recorded answers differ in the last bits, worst 12 ULP", "workbook_corpus": { "cells": 6, "last_bit": 2, "matched": 4, "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#L217-L222" ], "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#L217-L222", "state": "close", "suite": null, "summary": "Close: 46 of 68 recorded answers differ in the last bits, worst 12 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.BETAINV.json", "name": "BETAINV", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[BETA.INV](FUNC.BETA.INV.md) is the current spelling. [BETADIST](FUNC.BETADIST.md) reverses the value/probability direction.\n\n\n", "how-to-implement": "\n1. Validate positive finite shapes, finite ordered bounds and the current helper’s probability range. Retain the documented legacy endpoint distinction above.\n2. Search z on `[0,1]` using the current regularized lower beta ratio `F(z)`. The source uses the [ordered-binary64 inverse search](FUNC.CHISQ.INV.RT.md#how-to-implement), with this increasing forward function and target p: bisect the endpoint encodings until adjacent and return the upper one.\n3. Keep the callback unchanged. Its interior call supplies `bratio(alpha,beta,z,D(1-z))`; an independently substituted beta routine changes the surface being inverted.\n4. Using ordinary binary64 stores, form `width=D(B-A)`, `scaled=D(z*width)` and `result=D(A+scaled)`. Apply worksheet publication. Do not contract the final multiplication and addition into an FMA.\n\nWith both shapes one, p=0.25 gives z about one quarter, width four and result three. With shapes two and one, `F(z)=z^2`; z about one half gives result four on the same interval.\n\nFor p=0, the current search’s usual strict lower-bracket invariant does not hold: its forward value at zero already equals the target. Without an endpoint shortcut the nonnegative encoding search can terminate at the smallest positive binary64 value. That explains the interval-dependent publication described above; it is a code-path analysis, not an Excel measurement.\n\nA mathematical implementation can handle p=0 explicitly or use a safeguarded Newton/bisection method. Those are different endpoint and stopping policies. Current beta forward errors, stored affine stages and remaining inverse mismatches still need their own comparisons before a whole-function claim.\n\n\n", "quirks": "\nNonpositive shapes and invalid bounds give `#NUM!`; nonnumeric arguments give `#VALUE!`. Microsoft’s legacy page excludes probability zero and admits one.\n\nThe current shared helper’s validation accepts `[0,1]`, but that is not a promise that probability zero publishes the lower bound in every interval. It has no explicit zero shortcut before its adjacent-value search. On the standard interval this can leave a subnormal result that the current publisher refuses; on two to six, the affine addition rounds the same tiny search value to two. A preview refusal describes the implementation’s limit, rather than a recorded Excel error.\n\nThe inverse’s result is a value in the supplied interval, not another probability. A and B are value bounds, while p remains on the probability scale.\n\n\n", "sources": "\n- [Microsoft: BETAINV function](https://support.microsoft.com/en-us/excel/functions/betainv-function), opened 6 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 ratio and ordered-value search](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`=BETAINV(0.25,1,1,2,6)` is about `3`. The shape-one beta is uniform on the interval two to six; one quarter of the interval reaches three.\n\n`=BETAINV(0.25,2,1,2,6)` is about `4`. Its standard CDF is `z^2`, so probability one quarter selects z one half, then `2+4*z=4`.\n\n\n", "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n| 19929 | Windows, bitness not recorded, CPU not recorded | 71 |\n| 20131 | Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics | 62 |\n\n- XC-BETAINV-001: build 19929 versus build 20131; 2 same-input pairs, 0 differing answers. Compared axes: excel-build. Numeric answers were compared by their recorded binary64 bits; other answers by typed value.\n\nAgreement on these compared inputs does not establish agreement on unmeasured inputs.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.BETAINV.json).", "what-it-does": "\n`BETAINV(probability, alpha, beta, [A], [B])` finds a value whose cumulative beta probability is the requested probability. The two positive shape parameters control the distribution, and optional bounds A and B default to zero and one. This is a compatibility name.\n\n\n" }, "signature": { "display": "BETAINV(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": "Compatibility", "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": "Inverse of the cumulative beta distribution (the older form of BETA.INV)", "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/betainv-function-8b914ade-b902-43c1-ac9c-c05c54f10d6c" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "BETAINV" }, { "locale": "bg-BG", "name": "BETAINV" }, { "locale": "cs-CZ", "name": "BETAINV" }, { "locale": "da-DK", "name": "BETAINV" }, { "locale": "de-DE", "name": "BETAINV" }, { "locale": "el-GR", "name": "BETAINV" }, { "locale": "en-AU", "name": "BETAINV" }, { "locale": "en-GB", "name": "BETAINV" }, { "locale": "en-US", "name": "BETAINV" }, { "locale": "es-ES", "name": "DISTR.BETA.INV" }, { "locale": "et-EE", "name": "BETAINV" }, { "locale": "fi-FI", "name": "BEETAJAKAUMA.KÄÄNT" }, { "locale": "fr-FR", "name": "BETA.INVERSE*" }, { "locale": "he-IL", "name": "BETAINV" }, { "locale": "hr-HR", "name": "BETAINV" }, { "locale": "hu-HU", "name": "INVERZ.BÉTA" }, { "locale": "id-ID", "name": "BETAINV" }, { "locale": "it-IT", "name": "BETAINV" }, { "locale": "ja-JP", "name": "BETAINV" }, { "locale": "ko-KR", "name": "BETAINV" }, { "locale": "lt-LT", "name": "BETAINV" }, { "locale": "lv-LV", "name": "BETAINV" }, { "locale": "nb-NO", "name": "BETAINV" }, { "locale": "nl-NL", "name": "BETAINV" }, { "locale": "pl-PL", "name": "ROZKŁAD.BETA.ODW" }, { "locale": "pt-BR", "name": "BETAINV" }, { "locale": "pt-PT", "name": "BETA.ACUM.INV" }, { "locale": "ro-RO", "name": "BETAINV" }, { "locale": "ru-RU", "name": "БЕТАОБР" }, { "locale": "sk-SK", "name": "BETAINV" }, { "locale": "sl-SI", "name": "BETAINV" }, { "locale": "sr-Latn-RS", "name": "BETAINV" }, { "locale": "sv-SE", "name": "BETAINV" }, { "locale": "th-TH", "name": "BETAINV" }, { "locale": "tr-TR", "name": "BETATERS işlevi" }, { "locale": "uk-UA", "name": "BETAINV" }, { "locale": "vi-VN", "name": "BETAINV" }, { "locale": "zh-CN", "name": "BETAINV" }, { "locale": "zh-HK", "name": "BETAINV" }, { "locale": "zh-TW", "name": "BETAINV" } ], "signature": { "display": "BETAINV(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": "BETAINV", "version_marker": null, "xlcall": { "code": "272", "symbol": "xlfBetainv" } }, "microsoft": "https://support.microsoft.com/en-us/office/betainv-function-8b914ade-b902-43c1-ac9c-c05c54f10d6c" }, "try_it": { "formula": "=BETAINV(0.25,1,1,2,6)" }, "url": "https://handbook.dnacalc.com/functions/BETAINV.html", "variants": [], "versions": [ { "behaviour": "71 captured inputs are indexed for this environment. Capture dates are not recorded. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 19929", "platform": "Windows, bitness not recorded, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.BETAINV.json" ] }, { "behaviour": "62 captured inputs are indexed for this environment. Capture dates: 2026-07-17 to 2026-07-17. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20131", "platform": "Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.BETAINV.json" ] } ] }