feat: add stats/base/dists/log-logistic/cdf

[parthodas23]

Resolves none

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This pull request:

• feat: add stats/base/dists/log-logistic/cdf

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This pull request has the following related issues:

• RFC: add the log-logistic distribution #175

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Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/log-logistic/cdf	$\color{green}303/303$ $\color{green}+0.00%$	$\color{green}25/25$ $\color{green}+0.00%$	$\color{green}4/4$ $\color{green}+0.00%$	$\color{green}303/303$ $\color{green}+0.00%$

The above coverage report was generated for the changes in this PR.

[rautelaKamal]

Hey @parthodas23, pulling this down to review since I am also doing C-ports for distributions.

Found a subtle numerical overflow issue in src/main.c around lines 51-52:
xb = stdlib_base_pow( x / alpha, beta );
return xb / ( 1.0 + xb );

If x or beta is large enough, xb will overflow to Infinity. In C, calculating Infinity / (1.0 + Infinity) will evaluate to NaN instead of capping at 1.0.

You can actually prevent the overflow entirely by inverting the fraction analytically. If you compute it as:
return 1.0 / ( 1.0 + stdlib_base_pow( alpha / x, beta ) );

Then when x gets huge, alpha / x approaches 0.0, the denominator safely becomes 1.0, and the function returns 1.0 without any overflow or NaN issues.

Hope this helps! Happy to review again once you update.

[kgryte]

@rautelaKamal How does SciPy compute this quantity? While you are correct regarding rearranging terms, it is not just boundary behavior we need to be concerned about. For example, how does the rearrangement fair in terms of accuracy against reference implementations for the entire domain? Ideally, we'd be consistent with other libraries, such as those in Python/Julia here.

[parthodas23]

@kgryte I check SciPy's implementation (_continuous_distns.py) and @rautelaKamal was correct. I've updated src/main.c to use 1.0 / (1.0 + pow(alpha / x, beta)) to be consistent with SciPy.