{ "category": "Statistical functions", "display_name": "HYPGEOM.DIST", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.HYPGEOM.DIST", "implementation_state": { "answer_bank": { "excel_builds": [ "20430", "20527" ], "larger_numeric": 2, "last_bit": 176, "matched": 3483, "other_mismatch": 0, "refused": 0, "rows": 3661, "unread": 0, "worst_ulp": 23 }, "detail": "Of 3,759 recorded answers (3,661 in the answer bank and 98 workbook cells), 208 do not match: 4 differ by more than 16 ULP, 204 differ by at most 16 ULP.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "differs", "state_label": "Known larger differences", "summary": "Known larger differences on 208 of 3,759 recorded answers", "workbook_corpus": { "cells": 98, "larger_numeric": 2, "last_bit": 28, "matched": 68, "worst_ulp": 9 } }, "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#L290-L293" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/distributions::nums", "ported/discrete_dist::stirling_error", "ported/discrete_dist::deviance", "ported/discrete_dist::binom_mass", "ported/discrete_dist::finite", "ported/discrete_dist::hypergeom_mass", "ported/discrete_dist::hypergeom_dist_kernel", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_x87_add", "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::add", "ported/excel_numeric/x87::sub", "ported/excel_numeric/x87::div" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L290-L293", "state": "differs", "suite": null, "summary": "Known larger differences on 208 of 3,759 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.HYPGEOM.DIST.json", "name": "HYPGEOM.DIST", "notes": [ { "basis": "Read directly from four rows of the landed W111 domain capture. Its provenance names Excel build 20430, Windows 64-bit, Compatibility Version 2, exact-double bulk cell input and no cache. This harvest made no new Excel calls and did not compare builds.", "documentation": { "claim": "The opened HYPGEOM.DIST remarks specify #NUM! for a sample size or population success count at or below zero, and for sample successes above min(sample size,population successes).", "source": "https://support.microsoft.com/en-us/excel/functions/hypgeom-dist-function" }, "evidence": [ { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "hypgeom.dist-domain-01118-integer-support, hypgeom.dist-domain-01119-integer-support, hypgeom.dist-domain-01404-integer-support, hypgeom.dist-domain-01405-integer-support", "note": "Recorded answers and capture provenance.", "path": "runs/w111-distribution-domain-20260929/answers-hypgeom.dist.json.gz", "repository": "CalcFunc-Evidence" }, { "commit": "da3ecc4fb19a3a5529708c311d0e8f05688ac165", "locator": "hypergeom_mass and hypergeom_dist_kernel", "note": "Current support checks, degenerate masses and cumulative endpoint shortcut.", "path": "crates/calc-func/src/ported/discrete_dist.rs", "repository": "DnaCalc" } ], "functions": [ "FUNC.HYPGEOM.DIST" ], "inferred": null, "kind": "documentation-differs", "note_id": "FN-HYPGEOM.DIST-001", "open": [ "Whether every out-of-support and zero-count combination follows the same rule in other builds." ], "recorded_on": "2026-11-06", "repros": [ { "call": "HYPGEOM.DIST(0,0,0,5,0)", "correct": null, "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "sample_s", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "number_sample", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "population_s", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "number_pop", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "cumulative", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "hypgeom.dist-domain-01118-integer-support", "note": "Original capture provenance records cell_value2_bulk input plumbing and no cache use.", "path": "runs/w111-distribution-domain-20260929/answers-hypgeom.dist.json.gz", "repository": "CalcFunc-Evidence" } }, { "call": "HYPGEOM.DIST(0,0,0,5,1)", "correct": null, "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "sample_s", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "number_sample", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "population_s", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "number_pop", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "cumulative", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "hypgeom.dist-domain-01119-integer-support", "note": "Original capture provenance records cell_value2_bulk input plumbing and no cache use.", "path": "runs/w111-distribution-domain-20260929/answers-hypgeom.dist.json.gz", "repository": "CalcFunc-Evidence" } }, { "call": "HYPGEOM.DIST(5,4,2,5,0)", "correct": null, "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "sample_s", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "number_sample", "value": { "bits": "0x4010000000000000", "display": "4", "kind": "number" } }, { "name": "population_s", "value": { "bits": "0x4000000000000000", "display": "2", "kind": "number" } }, { "name": "number_pop", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "cumulative", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "hypgeom.dist-domain-01404-integer-support", "note": "Original capture provenance records cell_value2_bulk input plumbing and no cache use.", "path": "runs/w111-distribution-domain-20260929/answers-hypgeom.dist.json.gz", "repository": "CalcFunc-Evidence" } }, { "call": "HYPGEOM.DIST(5,4,2,5,1)", "correct": null, "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "sample_s", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "number_sample", "value": { "bits": "0x4010000000000000", "display": "4", "kind": "number" } }, { "name": "population_s", "value": { "bits": "0x4000000000000000", "display": "2", "kind": "number" } }, { "name": "number_pop", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "cumulative", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "hypgeom.dist-domain-01405-integer-support", "note": "Original capture provenance records cell_value2_bulk input plumbing and no cache use.", "path": "runs/w111-distribution-domain-20260929/answers-hypgeom.dist.json.gz", "repository": "CalcFunc-Evidence" } } ], "schema": "efh.function-note/v1", "statement": "Four retained build 20430 controls return numeric values where the opened documentation specifies #NUM!: HYPGEOM.DIST(0,0,0,5,0) and its cumulative form both return 1; HYPGEOM.DIST(5,4,2,5,0) returns 0 and its cumulative form returns 1. These observations cover the listed inputs, not every out-of-support call.", "status": "measured", "title": "Recorded hypergeometric calls admit zero counts and counts above the support" } ], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[HYPGEOMDIST](FUNC.HYPGEOMDIST.md) is the mass-only compatibility spelling. [BINOM.DIST](FUNC.BINOM.DIST.md) describes independent trials with one fixed probability, and [COMBIN](FUNC.COMBIN.md) counts selections.\n\n\n\n\n", "how-to-implement": "\nFor a mathematical implementation, count the supported selections:\n\n```text\nmass(k) = choose(K,k) * choose(N-K,n-k) / choose(N,n)\n```\n\nThe sample `k=1,n=2,K=3,N=5` has six favourable subsets out of ten, giving probability `0.6`. A recurrence between adjacent supported masses is a way to avoid constructing huge factorials, but it is an alternative algorithm.\n\nThe current compatibility candidate has a more specific composition:\n\n1. Reject original negative counts, then truncate all four toward zero. Reject `n>N` or `K>N`.\n2. For a mass, return zero for an unsupported `k`. Handle the degenerate `n=0` and `n=N` cases explicitly.\n3. Otherwise form the binary64 values `p=n/N` and `q=(N-n)/N` separately. Do not assume the stored `q` is interchangeable with `1-p`.\n4. Obtain shared binomial masses `a=b(k;K,p,q)`, `b=b(n-k;N-K,p,q)` and `c=b(n;N,p,q)`. Return `(a*b)/c` using the current binary64 multiplication and division order.\n5. For cumulative calls, the current code returns one immediately when `k>=min(n,K)`; otherwise it adds masses from zero through `k` and caps the sum at one.\n\nThe shared binomial body, small-tail choices and publication behaviour retain unresolved differences in the problem report. The generated fingerprint report says no complete hypergeometric algorithm is adopted. Treat this as a codeable current candidate, with the named recorded endpoint controls, rather than a whole-domain Excel identification.\n\n\n", "quirks": "\nThe feasible mathematical success interval is `max(0,n-(N-K))..min(n,K)`. Microsoft’s opened remarks specify `#NUM!` outside that interval and for nonpositive sample size, population success count or population size. Nonnumeric count arguments give `#VALUE!`.\n\nRecorded build 20430 controls depart from those stated guards. `HYPGEOM.DIST(0,0,0,5,0)` returned one. With successes above the support, `HYPGEOM.DIST(5,4,2,5,0)` returned zero, while changing the cumulative flag from zero to one returned one. [FN-HYPGEOM.DIST-001](../notes/FN-HYPGEOM.DIST-001.json) retains all four calls, exact inputs and provenance.\n\nThe current code checks original negative signs before truncating the counts, so a negative fraction must not become an admitted zero merely through truncation. Its support shortcuts and mass body need separate tests; neither the probability definition nor the public error list settles every recorded numerical edge.\n\n\n", "sources": "\n- [Microsoft: HYPGEOM.DIST function](https://support.microsoft.com/en-us/excel/functions/hypgeom-dist-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/discrete_dist.rs); implementation steps and the limits identified in the text.\n- [Public recorded domain bank](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/runs/w111-distribution-domain-20260929/answers-hypgeom.dist.json.gz); download and decompress the gzip JSON.\n- [Unresolved numerical scope](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/docs/generated/numeric-fingerprints.md) and [problem-function report](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/docs/generated/problem-functions.md).\n\n", "try-it": "\n`=HYPGEOM.DIST(1,2,3,5,FALSE)` is about `0.6`. Drawing two objects from five, three marked successful, yields one success in `choose(3,1)*choose(2,1)=6` of `choose(5,2)=10` possible samples.\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| 20430 | Windows, 64-bit, CPU not recorded | 3,653 |\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\nConcrete controls from the 29 September 2026 build 20430 capture:\n\n| Captured call | Excel result |\n|---|---:|\n| `HYPGEOM.DIST(0,0,0,5,0)` | 1 |\n| `HYPGEOM.DIST(0,0,0,5,1)` | 1 |\n| `HYPGEOM.DIST(5,4,2,5,0)` | 0 |\n| `HYPGEOM.DIST(5,4,2,5,1)` | 1 |\n\nInputs were written as exact doubles through bulk `Value2` cells. The capture records Windows 64-bit and Compatibility Version 2; it does not record CPU. These controls do not compare builds.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.HYPGEOM.DIST.json).", "what-it-does": "\n`HYPGEOM.DIST(sample_s, number_sample, population_s, number_pop, cumulative)` models a fixed-size sample drawn **without replacement** from a finite population. Every subset of the sample size has equal probability. FALSE returns the mass at exactly `sample_s` successes; TRUE returns the probability of at most that many.\n\nWrite the four counts as `k,n,K,N`: observed successes, sample size, population successes and population size. The success probability changes after each draw because the selected object is not replaced. A binomial model with one fixed probability answers a different sampling question.\n\n\n" }, "signature": { "display": "HYPGEOM.DIST(sample_s, number_sample, population_s, number_pop, cumulative)", "parameters": [ { "description": null, "name": "sample_s", "optional": false, "repeats": false }, { "description": null, "name": "number_sample", "optional": false, "repeats": false }, { "description": null, "name": "population_s", "optional": false, "repeats": false }, { "description": null, "name": "number_pop", "optional": false, "repeats": false }, { "description": null, "name": "cumulative", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 5, "min": 5 }, "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": "Hypergeometric distribution: the chance of k successes in a sample drawn without replacement", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the hypergeometric distribution", "microsoft_url": "https://support.microsoft.com/en-us/office/hypgeom-dist-function-6dbd547f-1d12-4b1f-8ae5-b0d9e3d22fbf" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "HYPGEOM.DIST" }, { "locale": "bg-BG", "name": "HYPGEOM.DIST" }, { "locale": "cs-CZ", "name": "HYPGEOM.DIST" }, { "locale": "da-DK", "name": "HYPGEO.FORDELING" }, { "locale": "de-DE", "name": "HYPGEOM.DIST" }, { "locale": "el-GR", "name": "HYPGEOM.DIST" }, { "locale": "en-AU", "name": "HYPGEOM.DIST" }, { "locale": "en-GB", "name": "HYPGEOM.DIST" }, { "locale": "en-US", "name": "HYPGEOM.DIST" }, { "locale": "es-ES", "name": "DISTR.HIPERGEOM.N" }, { "locale": "et-EE", "name": "HYPGEOM.DIST" }, { "locale": "fi-FI", "name": "HYPERGEOM_JAKAUMA" }, { "locale": "fr-FR", "name": "LOI.HYPERGEOMETRIQUE.N*" }, { "locale": "he-IL", "name": "HYPGEOM.DIST" }, { "locale": "hr-HR", "name": "HYPGEOM.DIST" }, { "locale": "hu-HU", "name": "HIPGEOM.ELOSZLÁS" }, { "locale": "id-ID", "name": "HYPGEOM.DIST" }, { "locale": "it-IT", "name": "HYPGEOM.DIST" }, { "locale": "ja-JP", "name": "HYPGEOM_DIST" }, { "locale": "ko-KR", "name": "HYPGEOM. DIST" }, { "locale": "lt-LT", "name": "HYPGEOM.DIST" }, { "locale": "lv-LV", "name": "HYPGEOM.DIST" }, { "locale": "nb-NO", "name": "HYPGEOM.FORDELING.N" }, { "locale": "nl-NL", "name": "HYPGEOM.VERD" }, { "locale": "pl-PL", "name": "ROZKŁ.HIPERGEOM" }, { "locale": "pt-BR", "name": "HYPGEOM.DIST" }, { "locale": "pt-PT", "name": "DIST.HIPGEOM" }, { "locale": "ro-RO", "name": "HYPGEOM.DIST" }, { "locale": "ru-RU", "name": "ГИПЕРГЕОМ.РАСП" }, { "locale": "sk-SK", "name": "HYPGEOM.DIST" }, { "locale": "sl-SI", "name": "HYPGEOM. DIST" }, { "locale": "sr-Latn-RS", "name": "HYPGEOM.DIST" }, { "locale": "sv-SE", "name": "HYPGEOM.FÖRD" }, { "locale": "th-TH", "name": "HYPGEOM.DIST" }, { "locale": "tr-TR", "name": "HİPERGEOM.DAĞ işlevi" }, { "locale": "uk-UA", "name": "HYPGEOM.DIST" }, { "locale": "vi-VN", "name": "HYPGEOM.DIST" }, { "locale": "zh-CN", "name": "HYPGEOM.DIST" }, { "locale": "zh-HK", "name": "HYPGEOM.DIST" }, { "locale": "zh-TW", "name": "HYPGEOM.DIST" } ], "signature": { "display": "HYPGEOM.DIST(sample_s, number_sample, population_s, number_pop, cumulative)", "parameters": [ { "description": null, "name": "sample_s", "optional": false, "repeats": false }, { "description": null, "name": "number_sample", "optional": false, "repeats": false }, { "description": null, "name": "population_s", "optional": false, "repeats": false }, { "description": null, "name": "number_pop", "optional": false, "repeats": false }, { "description": null, "name": "cumulative", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "HYPGEOM.DIST", "version_marker": null, "xlcall": { "code": "535", "symbol": "xlfHypgeom_dist" } }, "microsoft": "https://support.microsoft.com/en-us/office/hypgeom-dist-function-6dbd547f-1d12-4b1f-8ae5-b0d9e3d22fbf" }, "try_it": { "formula": "=HYPGEOM.DIST(1,2,3,5,FALSE)" }, "url": "https://handbook.dnacalc.com/functions/HYPGEOM.DIST.html", "variants": [], "versions": [ { "behaviour": "Recorded zero-count calls returned 1, and the sampled above-support call returned mass 0 and CDF 1. Four exact controls are attached from build 20430; no cross-build comparison was made.", "excel_build": "16.0 build 20430", "observations": [ { "call": "HYPGEOM.DIST(0,0,0,5,0)", "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "sample_s", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "number_sample", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "population_s", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "number_pop", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "cumulative", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026." }, { "call": "HYPGEOM.DIST(0,0,0,5,1)", "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "sample_s", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "number_sample", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "population_s", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } }, { "name": "number_pop", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "cumulative", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026." }, { "call": "HYPGEOM.DIST(5,4,2,5,0)", "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "sample_s", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "number_sample", "value": { "bits": "0x4010000000000000", "display": "4", "kind": "number" } }, { "name": "population_s", "value": { "bits": "0x4000000000000000", "display": "2", "kind": "number" } }, { "name": "number_pop", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "cumulative", "value": { "bits": "0x0000000000000000", "display": "0", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026." }, { "call": "HYPGEOM.DIST(5,4,2,5,1)", "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "sample_s", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "number_sample", "value": { "bits": "0x4010000000000000", "display": "4", "kind": "number" } }, { "name": "population_s", "value": { "bits": "0x4000000000000000", "display": "2", "kind": "number" } }, { "name": "number_pop", "value": { "bits": "0x4014000000000000", "display": "5", "kind": "number" } }, { "name": "cumulative", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit (NT 10.00), Workbook Compatibility Version 2; CPU not recorded. Captured 29 September 2026." } ], "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.HYPGEOM.DIST.json", "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/runs/w111-distribution-domain-20260929/answers-hypgeom.dist.json.gz" ] } ] }