Implement binomial, Poisson, and negative binomial inverse functions in pure Julia#205
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…in pure Julia Replace Rmath-dependent inverse functions for three discrete distributions with pure Julia implementations based on VBA code by Ian Smith: - Binomial: binominvcdf, binominvccdf, binominvlogcdf, binominvlogccdf - Poisson: poisinvcdf, poisinvccdf, poisinvlogcdf, poisinvlogccdf - Negative binomial: nbinominvcdf, nbinominvccdf, nbinominvlogcdf, nbinominvlogccdf All use normal approximation for initial guess followed by linear search with direct PMF evaluation. Each search function uses its own CDF variant (cdf or ccdf) directly, avoiding precision loss from 1-p subtraction. The invlog variants use -expm1(lq) when lq is close to 0. Tests use self-consistency round-trips for inverse functions, since our CDF implementation differs from Rmath's by ~1 ULP which can flip discrete answers.
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Codecov Report❌ Patch coverage is
Additional details and impacted files@@ Coverage Diff @@
## master #205 +/- ##
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+ Coverage 72.39% 76.04% +3.65%
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Files 22 22
Lines 1007 1269 +262
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+ Hits 729 965 +236
- Misses 278 304 +26 ☔ View full report in Codecov by Sentry. 🚀 New features to boost your workflow:
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Summary
Replace Rmath-dependent inverse functions for three discrete distributions with pure Julia implementations based on VBA code by Ian Smith:
binominvcdf,binominvccdf,binominvlogcdf,binominvlogccdfpoisinvcdf,poisinvccdf,poisinvlogcdf,poisinvlogccdfnbinominvcdf,nbinominvccdf,nbinominvlogcdf,nbinominvlogccdfAll use normal approximation for initial guess followed by linear search with direct PMF evaluation. Each search function uses its own CDF variant (cdf or ccdf) directly, avoiding precision loss from
1-psubtraction. Theinvlogvariants use-expm1(lq)whenlqis close to 0.Test plan
invcdf(cdf(k)) == kfor all support points with non-degenerate CDF valuesinvloground-trips allow ±1 tolerance due to inherentexp(log(cdf))precision loss🤖 Generated with Claude Code