Regularized incomplete gamma function (C backend) — core_gamma

The lower regularized incomplete gamma function \(P(a, x)\), which is the CDF of a Gamma distribution with shape a and unit rate. Exposed because it is the building block of the chi-square tail used by drift_chisq() and benford_test().

Usage

core_gamma_cdf(shape, x)

Arguments

shape: Shape parameter \(a\) (length-1, > 0).
x: Numeric vector of quantiles (>= 0).

Value

A numeric vector the length of x, each entry in \ [0, 1].

[0, 1]: R:0,%201%5C

Examples

core_gamma_cdf(3.5, c(0.5, 1, 4, 12))
#> [1] 0.005171463 0.040159631 0.667406097 0.998860649

# Identical to the unit-rate gamma CDF.
all.equal(core_gamma_cdf(3.5, c(0.5, 1, 4, 12)),
          stats::pgamma(c(0.5, 1, 4, 12), shape = 3.5))
#> [1] TRUE

# Shape 1 is the exponential distribution.
all.equal(core_gamma_cdf(1, c(0.5, 2)), stats::pexp(c(0.5, 2)))
#> [1] TRUE

# A chi-square tail on k degrees of freedom is 1 - P(k/2, q/2).
1 - core_gamma_cdf(2 / 2, 5.99 / 2)      # about 0.05 on 2 df
#> [1] 0.05003663