First two moments of the NB unit deviance, by direct summation

Reproduces the definition edgeR's compute_weight() approximates with Chebyshev tables. The summation window is centred on mu and sized from the pmf's own quantiles rather than fixed at edgeR's 50 terms from zero: edgeR can truncate there because that branch is only reached when phi >= 4, where the pmf piles up near zero; this is reached with any dispersion.

Usage

nbDevianceMoments(mu, phi, eps = 1e-10, maxterms = 20000L)

Arguments

mu

vector of means.

phi

NB dispersion: scalar, or the same length as mu.

eps

tail probability left outside the summation window at each end.

maxterms

hard cap on the number of pmf terms summed per element.

Value

list with w0 (deviance rescaling) and w1 (effective df), each the length of mu.

Details

Elements are grouped by the width they need so a few high-mu cells do not impose their window on everything, and each group accumulates in two passes so memory stays O(length(mu)) rather than O(width * length(mu)).

Examples

nbDevianceMoments(mu = c(0.1, 1, 10), phi = 5)
#> $w0
#> [1] 1.788589 4.251873 3.001213
#> 
#> $w1
#> [1] 0.5233816 2.8091676 2.8650045
#>