GAMMA.INV silently returned the first bisection midpoint for alpha in
~[143, 171.62] (e.g. GAMMA.INV(0.5, 143, 1) gave 358.0 instead of
142.667) and #NUM! above that, because the Newton-step pdf evaluates
Gamma(a), b**a and value**(a-1) in linear domain, all of which overflow
even though the density itself is a small representable number. The same
pattern breaks the GAMMA.DIST, CHISQ.DIST and F.DIST densities and
GAMMALN, which computed log(Gamma(x)) through Gamma(x).
Evaluate these in log domain via the existing logGamma, and scale the
incomplete-gamma series/continued-fraction iteration cap as O(sqrt(a)),
which both expansions need to converge near x ~ a once the shape is
large (GAMMA.INV drifted from the true quantile above alpha ~5000 and
returned alpha+1 by alpha=10000; same for CHISQ.INV at high df).
The incomplete gamma primitive used a fixed 32-term power series with no
convergence test, so GAMMA.DIST, GAMMADIST, CHISQ.DIST(.RT), GAMMAINV and
CHISQ.INV were grossly wrong once the series argument reached ~32
(e.g. CHISQ.DIST.RT(80, 4) returned 0.806 instead of 1.74e-16).
Replace it with the standard convergence-tested regularized incomplete
gamma: series P(a,x) for x < a+1, continued fraction Q(a,x) for x >= a+1.
CHISQ.DIST.RT now uses Q directly so the right tail stays free of
1 - P cancellation. Consolidates the duplicate copy that already existed
privately in ChiSquared onto the shared primitive.
While we might never be able to have 100% of our code strict, we can at
the very least do it for all of our tests. This ensures that our tests
are using our API with the types as intended by the test author, and not
silently be cast to what our API requires.
* First steps toward refactoring Statistical Distributions into smaller classes: BETA() and GAMMA() (and related functions) to start with... they all need a lot of tidying up, and more testing; but it's a start
* Add basic datatype validations to Beta and Gamma Excel function implementations
* Switch to using a trait with the validation methods to provide easier sharing between distribution classes
* Additional unit tests for Beta and Gamma functions, including unhappy path for validations
* Extract ChiSquared functions
* Additional argument validation checks with unit tests for Chi Squared functions
* Extract Fisher
* Move MEDIAN() and MODE() to the Averages class
* Extract filters for Median and Mode for common usage
* Merge branch 'master' of C:\Projects\PHPOffice\PHPSpreadsheet\develop with conflicts.
* New statistical tests
* Sniffs
* Additional statistical function unit tests
* Additional statistical function unit tests
* Fix case-sensitivity
* Fix HARMEAN code logic
* Unit tests refactored into individual files for all logical functions
Implemented IFNA()
* Fix silly typo
* NOT needs ...args to allow for test when no argument passed
* Codestyle
* Use instance asserts
Vincent Gao
Adrien Crivelli
Mark Baker