GAMMA.DIST

Microsoft publishes '=GAMMA.DIST(A2,A3,A4,FALSE)' with the result 0.032639. Derived independently with mpmath at 50 digits straight from the density the page states in prose -- x^(alpha-1) * e^(-x/beta) / (beta^alpha * Gamma(alpha)) -- rather than from any statistics library's gamma routine: with x = 10.00001131, alpha = 9, beta = 2 the value is 0.032639130418294001533, which rounds to exactly the published 0.032639. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft publishes '=GAMMA.DIST(A2,A3,A4,TRUE)' with the result 0.068094. Derived independently as the REGULARIZED LOWER INCOMPLETE GAMMA function P(alpha, x/beta) = P(9, 5.000005655) = 0.068094003869787331102 at 50 digits, which rounds to exactly the published 0.068094. Asserted at 12 dp: the 11th and 12th decimals (…3870) are carried because they are inside double precision and pin the implementation's incomplete-gamma routine, not just its leading digits. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft's GAMMA.DIST page states "When alpha = 1, GAMMA.DIST returns the exponential distribution with:" followed by an equation rendered as an image. The identity behind it is standard and independently checkable: the gamma CDF with alpha = 1 and scale beta is 1 - e^(-x/beta). At x = 2, beta = 3 that is 1 - e^(-2/3) = 0.48658288096740797313 (mpmath, 50 digits), and the regularized incomplete gamma P(1, 2/3) gives the identical value. Asserted as a difference of zero against the engine's OWN EXP, so it tests the distribution rather than a printed constant, and so it holds even if the engine's exp differs in the last bit. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft's GAMMA.DIST page states: "For a positive integer n, when alpha = n/2, beta = 2, and cumulative = TRUE, GAMMA.DIST returns (1 - CHISQ.DIST.RT(x)) with n degrees of freedom." Instantiated here at n = 4, so alpha = 2 and beta = 2. Derived independently: P(2, 1.5) = 0.44217459962892543 at 50 digits, and the chi-squared survival function at x = 3 with 4 degrees of freedom is 0.55782540037107457, whose complement is the same number. Written as a difference of exactly zero so it tests the two functions against each other inside the engine under test rather than against a figure from outside it. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If x < 0, GAMMA.DIST returns the #NUM! error value." The gamma distribution has no support below zero. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #NUM! -- the same systemic #VALUE!-substitution pattern already recorded across this corpus, an error-code difference rather than a computation one. WORTH READING NEXT TO ITS LEGACY TWIN: on the identical input, LibreOffice's GAMMADIST(-1,9,2,TRUE) returns the NUMBER 0 rather than any error at all (see data/tests/GAMMADIST.json). The two names are documented as the same function with the same exclusions, but LibreOffice guards the modern spelling and not the legacy one, so which spelling a workbook happens to use decides whether an out-of-domain x is visible.

Excel documents: "If alpha <= 0 or if beta <= 0, GAMMA.DIST returns the #NUM! error value." Zero is the boundary of the exclusion. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #NUM! -- the same systemic #VALUE!-substitution pattern already recorded across this corpus, an error-code difference rather than a computation one. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If alpha <= 0 or if beta <= 0, GAMMA.DIST returns the #NUM! error value." Asserted separately from the alpha case because an engine can guard one parameter and not the other; beta also appears in a division (x/beta), so a missing guard here surfaces as #DIV/0! rather than a wrong number. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #NUM! -- the same systemic #VALUE!-substitution pattern already recorded across this corpus, an error-code difference rather than a computation one. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If x, alpha, or beta is nonnumeric, GAMMA.DIST returns the #VALUE! error value." Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft publishes '=GAMMA.DIST(A2,A3,A4,FALSE)' with the result 0.032639. Derived independently with mpmath at 50 digits straight from the density the page states in prose -- x^(alpha-1) * e^(-x/beta) / (beta^alpha * Gamma(alpha)) -- rather than from any statistics library's gamma routine: with x = 10.00001131, alpha = 9, beta = 2 the value is 0.032639130418294001533, which rounds to exactly the published 0.032639. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft publishes '=GAMMA.DIST(A2,A3,A4,TRUE)' with the result 0.068094. Derived independently as the REGULARIZED LOWER INCOMPLETE GAMMA function P(alpha, x/beta) = P(9, 5.000005655) = 0.068094003869787331102 at 50 digits, which rounds to exactly the published 0.068094. Asserted at 12 dp: the 11th and 12th decimals (…3870) are carried because they are inside double precision and pin the implementation's incomplete-gamma routine, not just its leading digits. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft's GAMMA.DIST page states "When alpha = 1, GAMMA.DIST returns the exponential distribution with:" followed by an equation rendered as an image. The identity behind it is standard and independently checkable: the gamma CDF with alpha = 1 and scale beta is 1 - e^(-x/beta). At x = 2, beta = 3 that is 1 - e^(-2/3) = 0.48658288096740797313 (mpmath, 50 digits), and the regularized incomplete gamma P(1, 2/3) gives the identical value. Asserted as a difference of zero against the engine's OWN EXP, so it tests the distribution rather than a printed constant, and so it holds even if the engine's exp differs in the last bit. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft's GAMMA.DIST page states: "For a positive integer n, when alpha = n/2, beta = 2, and cumulative = TRUE, GAMMA.DIST returns (1 - CHISQ.DIST.RT(x)) with n degrees of freedom." Instantiated here at n = 4, so alpha = 2 and beta = 2. Derived independently: P(2, 1.5) = 0.44217459962892543 at 50 digits, and the chi-squared survival function at x = 3 with 4 degrees of freedom is 0.55782540037107457, whose complement is the same number. Written as a difference of exactly zero so it tests the two functions against each other inside the engine under test rather than against a figure from outside it. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If x < 0, GAMMA.DIST returns the #NUM! error value." The gamma distribution has no support below zero. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #NUM! -- the same systemic #VALUE!-substitution pattern already recorded across this corpus, an error-code difference rather than a computation one. WORTH READING NEXT TO ITS LEGACY TWIN: on the identical input, LibreOffice's GAMMADIST(-1,9,2,TRUE) returns the NUMBER 0 rather than any error at all (see data/tests/GAMMADIST.json). The two names are documented as the same function with the same exclusions, but LibreOffice guards the modern spelling and not the legacy one, so which spelling a workbook happens to use decides whether an out-of-domain x is visible.

Excel documents: "If alpha <= 0 or if beta <= 0, GAMMA.DIST returns the #NUM! error value." Zero is the boundary of the exclusion. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #NUM! -- the same systemic #VALUE!-substitution pattern already recorded across this corpus, an error-code difference rather than a computation one. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If alpha <= 0 or if beta <= 0, GAMMA.DIST returns the #NUM! error value." Asserted separately from the alpha case because an engine can guard one parameter and not the other; beta also appears in a division (x/beta), so a missing guard here surfaces as #DIV/0! rather than a wrong number. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #NUM! -- the same systemic #VALUE!-substitution pattern already recorded across this corpus, an error-code difference rather than a computation one. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If x, alpha, or beta is nonnumeric, GAMMA.DIST returns the #VALUE! error value." Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft publishes '=GAMMA.DIST(A2,A3,A4,FALSE)' with the result 0.032639. Derived independently with mpmath at 50 digits straight from the density the page states in prose -- x^(alpha-1) * e^(-x/beta) / (beta^alpha * Gamma(alpha)) -- rather than from any statistics library's gamma routine: with x = 10.00001131, alpha = 9, beta = 2 the value is 0.032639130418294001533, which rounds to exactly the published 0.032639. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft publishes '=GAMMA.DIST(A2,A3,A4,TRUE)' with the result 0.068094. Derived independently as the REGULARIZED LOWER INCOMPLETE GAMMA function P(alpha, x/beta) = P(9, 5.000005655) = 0.068094003869787331102 at 50 digits, which rounds to exactly the published 0.068094. Asserted at 12 dp: the 11th and 12th decimals (…3870) are carried because they are inside double precision and pin the implementation's incomplete-gamma routine, not just its leading digits. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft's GAMMA.DIST page states "When alpha = 1, GAMMA.DIST returns the exponential distribution with:" followed by an equation rendered as an image. The identity behind it is standard and independently checkable: the gamma CDF with alpha = 1 and scale beta is 1 - e^(-x/beta). At x = 2, beta = 3 that is 1 - e^(-2/3) = 0.48658288096740797313 (mpmath, 50 digits), and the regularized incomplete gamma P(1, 2/3) gives the identical value. Asserted as a difference of zero against the engine's OWN EXP, so it tests the distribution rather than a printed constant, and so it holds even if the engine's exp differs in the last bit. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft's GAMMA.DIST page states: "For a positive integer n, when alpha = n/2, beta = 2, and cumulative = TRUE, GAMMA.DIST returns (1 - CHISQ.DIST.RT(x)) with n degrees of freedom." Instantiated here at n = 4, so alpha = 2 and beta = 2. Derived independently: P(2, 1.5) = 0.44217459962892543 at 50 digits, and the chi-squared survival function at x = 3 with 4 degrees of freedom is 0.55782540037107457, whose complement is the same number. Written as a difference of exactly zero so it tests the two functions against each other inside the engine under test rather than against a figure from outside it. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If x < 0, GAMMA.DIST returns the #NUM! error value." The gamma distribution has no support below zero. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #NUM! -- the same systemic #VALUE!-substitution pattern already recorded across this corpus, an error-code difference rather than a computation one. WORTH READING NEXT TO ITS LEGACY TWIN: on the identical input, LibreOffice's GAMMADIST(-1,9,2,TRUE) returns the NUMBER 0 rather than any error at all (see data/tests/GAMMADIST.json). The two names are documented as the same function with the same exclusions, but LibreOffice guards the modern spelling and not the legacy one, so which spelling a workbook happens to use decides whether an out-of-domain x is visible.

Excel documents: "If alpha <= 0 or if beta <= 0, GAMMA.DIST returns the #NUM! error value." Zero is the boundary of the exclusion. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #NUM! -- the same systemic #VALUE!-substitution pattern already recorded across this corpus, an error-code difference rather than a computation one. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If alpha <= 0 or if beta <= 0, GAMMA.DIST returns the #NUM! error value." Asserted separately from the alpha case because an engine can guard one parameter and not the other; beta also appears in a division (x/beta), so a missing guard here surfaces as #DIV/0! rather than a wrong number. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #NUM! -- the same systemic #VALUE!-substitution pattern already recorded across this corpus, an error-code difference rather than a computation one. Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If x, alpha, or beta is nonnumeric, GAMMA.DIST returns the #VALUE! error value." Set up from Microsoft's own worked-example table: A2 = 10.00001131 (the value at which the distribution is evaluated), A3 = 9 (alpha) and A4 = 2 (beta), pasted at A1 exactly as the page describes. Column F is untouched because this harness writes the formula under test into cell F1.