{ "category": "Statistical functions", "display_name": "GAMMA.INV", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.GAMMA.INV", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "?" ], "larger_numeric": 7, "last_bit": 147, "matched": 50, "other_mismatch": 0, "refused": 0, "rows": 204, "unread": 0, "worst_ulp": 55 }, "detail": "Of 209 recorded answers (204 in the answer bank and 5 workbook cells), 155 do not match: 7 differ by more than 16 ULP, 148 differ by at most 16 ULP.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "differs", "state_label": "Known larger differences", "summary": "Known larger differences on 155 of 209 recorded answers", "workbook_corpus": { "cells": 5, "last_bit": 1, "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#L231-L234" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/distributions::nums", "ported/beta_gamma_stats_family::validate_gamma_shape", "ported/beta_gamma_stats_family::gamma_inv_kernel", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_expm1_internal", "ported/excel_numeric::expm1_internal_graph", "ported/excel_numeric::excel_x87_sub", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_x87_temme_finish", "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_math_common::gratio_norm_gamma", "ported/special_math_common::gratio_rexp", "ported/special_math_common::gratio_rlog", "ported/special_math_common::gratio_gam1", "ported/special_math_common::gratio", "ported/special_math_common::series_prefactor", "ported/special_math_common::gratio_after40", "ported/special_math_common::gratio_cf", "ported/special_math_common::gratio_temme_270", "ported/special_math_common::gratio_temme_340", "ported/special_math_common::gratio_temme_330", "ported/special_math_common::gratio_temme_finish", "ported/special_math_common::regularized_gamma_p", "ported/special_math_common::bisect_inverse" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L231-L234", "state": "differs", "suite": null, "summary": "Known larger differences on 155 of 209 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.GAMMA.INV.json", "name": "GAMMA.INV", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[GAMMA.DIST](FUNC.GAMMA.DIST.md) supplies the forward distribution. [GAMMAINV](FUNC.GAMMAINV.md) is the compatibility spelling. [CHISQ.INV](FUNC.CHISQ.INV.md) uses gamma shape df/2 and scale two; [BETA.INV](FUNC.BETA.INV.md) inverts a bounded distribution.\n\n\n", "how-to-implement": "\n1. Validate finite positive alpha and beta and finite p. Return zero for p=0; reject p<0 or p>=1 under the current endpoint rule.\n2. With ordinary binary64 operations, initialize `lo=0` and `hi=beta*max(alpha+10*sqrt(alpha)+10,1)`.\n3. Evaluate `F(x)=regularized_gamma_p(alpha,D(x/beta))`. While F(hi) is below p, double hi. The current source permits 200 expansion checks; extreme-parameter bracketing and nonfinite callbacks remain explicit limitations.\n4. Bisect the nonnegative binary64 encodings of lo and hi, as in the [shared ordered-value inverse recipe](FUNC.CHISQ.INV.RT.md#how-to-implement). If F(mid)>=p keep the midpoint as the upper endpoint; otherwise keep it as lower. Return the upper value when the endpoint encodings are adjacent.\n5. Apply worksheet numeric publication. The candidate searches x on its scaled interval; it does not simply solve once at scale one and multiply an already rounded answer by beta.\n\nFor alpha=1, beta=2 and p=0.5, the mathematical equation gives about `1.38629436111989`. That explains the example. Its numerical candidate still depends on the generic forward callback and upper-adjacent return, rather than an exact inverse exponential formula.\n\nA bracketed Newton method or a residual-based stopping rule is another reasonable mathematical solver. Changing the callback to the public CDF’s special branches is also a separate numerical candidate. Forward-ratio errors, conditioning in the tails, bracket extremes and remaining inverse mismatches remain open; no whole-function Handbook suite is published.\n\n\n", "quirks": "\nMicrosoft documents `#VALUE!` for a text argument, `#NUM!` for nonpositive shape or scale and for p outside zero to one. The current helper returns zero at p=0 and `#NUM!` at p=1, where there is no finite mathematical gamma quantile.\n\nThe opened modern page documents an iterative search limit of 64 tries followed by `#N/A`; the legacy GAMMAINV page describes 100 tries. This documentation difference is not a measured change between named Excel builds, and the current helper uses its own bracket and adjacent-value search.\n\nThe current inverse callback is the generic lower gamma ratio. It does not call the public GAMMA.DIST wrapper, whose half-shape and shape-one cases have separate ERF and exponential paths.\n\n\n", "sources": "\n- [Microsoft: GAMMA.INV function](https://support.microsoft.com/en-us/excel/functions/gamma-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- [Generic gamma ratio and ordered-value search](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/special_math_common.rs); callback and adjacent binary64 return.\n- [Remaining numerical failures](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/docs/generated/problem-functions.md).\n\n", "try-it": "\n`=GAMMA.INV(0.5,1,2)` is about `1.3862943611`. The mathematical shape-one CDF is `1-exp(-x/2)`, so its median solves `x=-2*ln(0.5)`.\n\n`=GAMMA.INV(0.5,1,4)` is about `2.7725887222`. Doubling the scale doubles the mathematical quantile, though the current search has its own stored path.\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| 20131 | Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics | 204 |\n\nThe record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.GAMMA.INV.json).", "what-it-does": "\n`GAMMA.INV(probability,alpha,beta)` returns a gamma-distribution quantile for positive shape alpha and positive scale beta. It seeks the x whose lower cumulative probability is the requested p. Beta scales x’s units, rather than supplying an exponential rate.\n\n\n" }, "signature": { "display": "GAMMA.INV(probability, alpha, beta)", "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 } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 3, "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 gamma distribution reaches a given probability", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the inverse of the gamma cumulative distribution", "microsoft_url": "https://support.microsoft.com/en-us/office/gamma-inv-function-74991443-c2b0-4be5-aaab-1aa4d71fbb18" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "GAMMA.INV" }, { "locale": "bg-BG", "name": "GAMMA.INV" }, { "locale": "cs-CZ", "name": "GAMMA.INV" }, { "locale": "da-DK", "name": "GAMMA.INV" }, { "locale": "de-DE", "name": "GAMMA.INV" }, { "locale": "el-GR", "name": "GAMMA.INV" }, { "locale": "en-AU", "name": "GAMMA.INV" }, { "locale": "en-GB", "name": "GAMMA.INV" }, { "locale": "en-US", "name": "GAMMA.INV" }, { "locale": "es-ES", "name": "INV.GAMMA" }, { "locale": "et-EE", "name": "GAMMA.INV" }, { "locale": "fi-FI", "name": "GAMMA.JAKAUMA.KÄÄNT" }, { "locale": "fr-FR", "name": "LOI.GAMMA.INVERSE.N*" }, { "locale": "he-IL", "name": "GAMMA.INV" }, { "locale": "hr-HR", "name": "GAMMA.INV" }, { "locale": "hu-HU", "name": "GAMMA.INVERZ" }, { "locale": "id-ID", "name": "GAMMA.INV" }, { "locale": "it-IT", "name": "GAMMA.INV" }, { "locale": "ja-JP", "name": "GAMMA.INV" }, { "locale": "ko-KR", "name": "GAMMA.INV" }, { "locale": "lt-LT", "name": "GAMMA.INV" }, { "locale": "lv-LV", "name": "GAMMA.INV" }, { "locale": "nb-NO", "name": "GAMMA.INV" }, { "locale": "nl-NL", "name": "GAMMA.INV.N" }, { "locale": "pl-PL", "name": "ROZKŁ.GAMMA.ODWR" }, { "locale": "pt-BR", "name": "GAMMA.INV" }, { "locale": "pt-PT", "name": "INV.GAMA" }, { "locale": "ro-RO", "name": "GAMMA.INV" }, { "locale": "ru-RU", "name": "ГАММА.ОБР" }, { "locale": "sk-SK", "name": "GAMMA.INV" }, { "locale": "sl-SI", "name": "GAMMA.INV" }, { "locale": "sr-Latn-RS", "name": "GAMMA.INV" }, { "locale": "sv-SE", "name": "GAMMA.INV" }, { "locale": "th-TH", "name": "GAMMA.INV" }, { "locale": "tr-TR", "name": "GAMA.TERS" }, { "locale": "uk-UA", "name": "GAMMA.INV" }, { "locale": "vi-VN", "name": "GAMMA.INV" }, { "locale": "zh-CN", "name": "GAMMA.INV" }, { "locale": "zh-HK", "name": "GAMMA.INV" }, { "locale": "zh-TW", "name": "GAMMA.INV" } ], "signature": { "display": "GAMMA.INV(probability, alpha, beta)", "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 } ], "trailing_repeats": false }, "surface_name": "GAMMA.INV", "version_marker": null, "xlcall": { "code": "496", "symbol": "xlfGamma_inv" } }, "microsoft": "https://support.microsoft.com/en-us/office/gamma-inv-function-74991443-c2b0-4be5-aaab-1aa4d71fbb18" }, "try_it": { "formula": "=GAMMA.INV(0.5,1,2)" }, "url": "https://handbook.dnacalc.com/functions/GAMMA.INV.html", "variants": [], "versions": [ { "behaviour": "204 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.GAMMA.INV.json" ] } ] }