GAMMADIST

What it does

GAMMADIST(x, alpha, beta, cumulative)

GAMMADIST(x,alpha,beta,cumulative) evaluates a gamma distribution with positive shape alpha and positive scale beta. TRUE returns the probability up to nonnegative x; FALSE returns a density. Beta has the same units as x. This is the compatibility spelling of GAMMA.DIST.

Shape one is the exponential waiting-time distribution with rate 1/beta. Shapes n/2 and scale two describe a chi-squared distribution with n degrees of freedom; these are mathematical relations, whose worksheet compositions can have different rounding histories.

Try it

=GAMMADIST(2,1,2,TRUE) is about 0.632120558828558. With shape one it is an exponential waiting-time CDF with scale two.

Quirks

Negative x or nonpositive shape or scale gives #NUM!; nonnumeric numeric arguments give #VALUE!. A scale of two is not an exponential rate of two: for shape one it corresponds to rate one half.

The zero-input density needs a separate boundary decision. Mathematically its right-hand limit is zero for alpha>1, 1/beta for alpha=1, and unbounded for 0<alpha<1. The current density fallback evaluates a log expression at zero and can give #NUM!, including at shape one. Do not use a mathematical boundary value as an uncited claim about Excel’s actual return.

How to implement

The current shared CDF route first forms the binary64 scale ratio y=x/beta:

1. At shape alpha=0.5, it calls the ERF.PRECISE body at the current binary64 sqrt(y).
2. At shape one, it calls the exponential CDF with arguments (y,1). Computing EXPON.DIST(x,1/beta,TRUE) instead forms a different rounded ratio/product.
3. Other shapes call the regularized lower gamma ratio P(alpha,y).

The source retains modern-spelling composition controls for the first two branches, including non-dyadic scales. They do not identify every general-shape branch, and the shape-one density is not established by the CDF identity.

For positive x with shape other than one, the current density candidate forms stored y=R(x/beta) and t=R(alpha*LN(y)), then obtains an exponential prefix corresponding to exp(t-y-logGamma(alpha+1)). It finally multiplies that prefix by the separately stored ratio R(alpha/x), with another stored multiplication. The outer ratio/product consumer has discriminating controls; the prefix producer and its return stage remain open. Shape one and zero input have separate fallback code.

For the example x=2,alpha=1,beta=2, y=1, so the mathematical CDF is 1-exp(-1), about 0.632120558828558. That reduction explains the probability; substituting an integer-shape finite sum, a host gamma library or a reciprocal scale is another numerical candidate. The problem report retains general distribution mismatches, and no whole-function Handbook suite is published.

Rust code

55 gammadist "GAMMADIST" (4, 4) [V "x", V "alpha", V "beta", V "cumulative"] |s, a, sv| {
    let [x, alpha, beta] = nums::<3>(s, a)?;
    out(s, bg::gamma_dist_kernel(x, alpha, beta, flag(s, a, 3)?))
}

No implementation has been published with a Handbook test suite for this function.

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.

The 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.

Recorded environments and comparison details.

Alternatives

GAMMA.DIST is the current spelling; EXPON.DIST handles the shape-one waiting time; CHISQ.DIST is a shape/scale specialization.

Named variants

No named variants are recorded yet.