feat: add LogLogisticDistribution (Fisk) — log-space Logistic pipeline, survival analysis (depends on #54)

[OldCrow]

Summary

Add the Log-Logistic (Fisk) distribution. Once LogisticDistribution (issue #54) is implemented, Log-Logistic is a log-space transformation of Logistic — the batch path reduces to vector_log + the Logistic SIMD pipeline.

Parametrisation

Shape α > 0, scale β > 0. Scipy: fisk. Support: x > 0.

z       = log(x/β) · α   (i.e. α · (log(x) - log(β)))
CDF(x)  = 1 / (1 + exp(-z))    = CDF_Logistic(z; μ=0, s=1)
PDF(x)  = (α/β) · (x/β)^(α-1) / (1 + (x/β)^α)²
log PDF = log(α) - log(β) + (α-1)·log(x/β) - 2·log(1 + (x/β)^α)

Batch CDF: vector_log(x) → scalar_multiply(α) → scalar_add(-α·log(β)) → Logistic CDF pipeline (vector_exp + arithmetic).

Properties

• Median = β
• Mean = β·π/(α·sin(π/α)) for α > 1; undefined for α ≤ 1
• Variance: closed form for α > 2
• Skewness: right-skewed for all α
• MLE: α estimated via Newton–Raphson on the log-likelihood profile score; β̂ = sample median
• Use cases: survival analysis (heavier tail than Weibull, lighter than Pareto), income distributions (Fisk 1961), hydrology

Implementation notes

• Prerequisite: issue feat: add LogisticDistribution and GumbelDistribution — closed-form SIMD via vector_exp #54 (LogisticDistribution). The batch CDF implementation reuses the Logistic CDF batch path after a log-transform pre-pass.
• The alternative direct formula CDF(x) = (x/β)^α / (1 + (x/β)^α) avoids a log+exp but loses precision for small x; the logistic form is numerically superior.
• Dispatch thresholds: NEVER initially. Expect thresholds similar to LogNormal (log + exp chain).
• is_delegation_wrapper = false — the implementation uses Logistic primitives but has its own parameterisation and moments.