{ "category": "Statistical functions", "display_name": "F.DIST.RT", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.F.DIST.RT", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "?" ], "larger_numeric": 0, "last_bit": 1, "matched": 5, "other_mismatch": 0, "refused": 0, "rows": 6, "unread": 0, "worst_ulp": 2 }, "detail": "Everything else matches (6 in the answer bank and 5 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: 2 of 11 recorded answers differ in the last bits, worst 2 ULP", "workbook_corpus": { "cells": 5, "last_bit": 1, "matched": 4, "worst_ulp": 1 } }, "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#L141-L144" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/distributions::nums", "ported/chi_f_t_family::truncate_positive_integer", "ported/chi_f_t_family::validate_nonnegative_x", "ported/chi_f_t_family::f_dist_rt_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" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L141-L144", "state": "close", "suite": null, "summary": "Close: 2 of 11 recorded answers differ in the last bits, worst 2 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.F.DIST.RT.json", "name": "F.DIST.RT", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[F.INV.RT](FUNC.F.INV.RT.md) maps an upper-tail probability to a critical value. [F.DIST](FUNC.F.DIST.md) provides the left CDF or density; [F.TEST](FUNC.F.TEST.md) starts with two samples.\n\n\n", "how-to-implement": "\nThe current right-tail route evaluates a lower beta ratio after swapping the degree roles. Use ordinary binary64 stores D.\n\n1. Validate finite nonnegative x and the truncated positive degree counts d1 and d2.\n2. Calculate `num=D(d1*x)` and `den=D(d2+num)`.\n3. Independently store `z=D(d2/den)` and `w=D(num/den)`. Pass both to `bratio(d2/2,d1/2,z,w)` and return its first, lower-ratio result. The explicit complement w is part of the current argument construction.\n4. Apply worksheet number publication, preserving the host’s error/refusal distinction.\n\nWith d1=d2=2 and x=3, num is six and den eight. The transformed beta shapes are one and one, a uniform distribution, so z=2/8 gives the right probability one quarter. The companion left route uses 6/8 instead.\n\nDo not obtain this tail by subtracting a rounded left CDF from one. A separately scaled ratio can avoid overflowing `d1*x` in a mathematical implementation, but changes the current computation tree. The paired-argument wrapper is more specific than a generic beta identity; the inner beta approximation and remaining recorded mismatches still prevent a whole-domain identification.\n\n\n", "quirks": "\nDegree counts are truncated. Microsoft documents `#VALUE!` for nonnumeric arguments and `#NUM!` for negative x or degree counts below one. The current shared helper also rejects a nonfinite x and a truncated degree count above `10^10`; that code cap is separate from the opened page’s lower-bound wording.\n\nThe left CDF rises from zero and the right tail falls from one. The density option in F.DIST is a third quantity, rather than either of those probabilities. At x=0 the current density gives `#NUM!` for numerator degree one, one for degree two and zero for higher degrees. Those density cases do not change the endpoint probabilities.\n\nThe current beta transformation forms the product of x and numerator degrees directly. Extreme products or beta/gamma approximations need their own numerical error and publication checks; a finite mathematical probability alone does not ensure this candidate evaluates it successfully.\n\n\n", "sources": "\n- [Microsoft: F.DIST.RT function](https://support.microsoft.com/en-us/excel/functions/f-dist-rt-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/chi_f_t_family.rs); implementation steps and the limits identified in the text.\n\n", "try-it": "\n`=F.DIST.RT(3,2,2)` is about `0.25`. With both degree counts two, the mathematical left CDF is `x/(1+x)` and the right tail is `1/(1+x)`.\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 | 6 |\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.F.DIST.RT.json).", "what-it-does": "\n`F.DIST.RT(x, deg_freedom1, deg_freedom2)` returns an F-distribution right-tail probability. The first degree count belongs to the numerator and the second to the denominator.\n\n\n" }, "signature": { "display": "F.DIST.RT(x, deg_freedom1, deg_freedom2)", "parameters": [ { "description": null, "name": "x", "optional": false, "repeats": false }, { "description": null, "name": "deg_freedom1", "optional": false, "repeats": false }, { "description": null, "name": "deg_freedom2", "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": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Right-tail probability of the F distribution", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the F probability distribution", "microsoft_url": "https://support.microsoft.com/en-us/office/f-dist-rt-function-d74cbb00-6017-4ac9-b7d7-6049badc0520" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "F.DIST.RT" }, { "locale": "bg-BG", "name": "F.DIST.RT" }, { "locale": "cs-CZ", "name": "F.DIST.RT" }, { "locale": "da-DK", "name": "F.FORDELING.RT" }, { "locale": "de-DE", "name": "F.DIST.RT" }, { "locale": "el-GR", "name": "F.DIST.RT" }, { "locale": "en-AU", "name": "F.DIST.RT" }, { "locale": "en-GB", "name": "F.DIST.RT" }, { "locale": "en-US", "name": "F.DIST.RT" }, { "locale": "es-ES", "name": "DISTR.F.CD" }, { "locale": "et-EE", "name": "F.DIST.RT" }, { "locale": "fi-FI", "name": "F.JAKAUMA.OH" }, { "locale": "fr-FR", "name": "LOI.F.DROITE*" }, { "locale": "he-IL", "name": "F.DIST.RT" }, { "locale": "hr-HR", "name": "F.DIST.RT" }, { "locale": "hu-HU", "name": "F.ELOSZLÁS.JOBB" }, { "locale": "id-ID", "name": "F.DIST.RT" }, { "locale": "it-IT", "name": "F.DIST.RT" }, { "locale": "ja-JP", "name": "F.DIST.RT" }, { "locale": "ko-KR", "name": "F.DIST.RT" }, { "locale": "lt-LT", "name": "F.DIST.RT" }, { "locale": "lv-LV", "name": "F.DIST.RT" }, { "locale": "nb-NO", "name": "F.DIST.RT" }, { "locale": "nl-NL", "name": "F.VERD.RECHTS" }, { "locale": "pl-PL", "name": "ROZKŁ.F.PS" }, { "locale": "pt-BR", "name": "F.DIST.RT" }, { "locale": "pt-PT", "name": "DIST.F.DIR" }, { "locale": "ro-RO", "name": "F.DIST.RT" }, { "locale": "ru-RU", "name": "F.РАСП.ПХ" }, { "locale": "sk-SK", "name": "F.DIST.RT" }, { "locale": "sl-SI", "name": "F.DIST. RT" }, { "locale": "sr-Latn-RS", "name": "F.DIST.RT" }, { "locale": "sv-SE", "name": "F.FÖRD.RT" }, { "locale": "th-TH", "name": "F.DIST.RT" }, { "locale": "tr-TR", "name": "F.DAĞ.SAĞK" }, { "locale": "uk-UA", "name": "F.DIST.RT" }, { "locale": "vi-VN", "name": "F.DIST.RT" }, { "locale": "zh-CN", "name": "F.DIST.RT" }, { "locale": "zh-HK", "name": "F.DIST.RT" }, { "locale": "zh-TW", "name": "F.DIST.RT" } ], "signature": { "display": "F.DIST.RT(x, deg_freedom1, deg_freedom2)", "parameters": [ { "description": null, "name": "x", "optional": false, "repeats": false }, { "description": null, "name": "deg_freedom1", "optional": false, "repeats": false }, { "description": null, "name": "deg_freedom2", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "F.DIST.RT", "version_marker": null, "xlcall": { "code": "532", "symbol": "xlfF_dist_rt" } }, "microsoft": "https://support.microsoft.com/en-us/office/f-dist-rt-function-d74cbb00-6017-4ac9-b7d7-6049badc0520" }, "try_it": { "formula": "=F.DIST.RT(3,2,2)" }, "url": "https://handbook.dnacalc.com/functions/F.DIST.RT.html", "variants": [], "versions": [ { "behaviour": "6 captured inputs are indexed for this environment. Capture dates: 2026-07-16 to 2026-07-16. 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.F.DIST.RT.json" ] } ] }