Optimization

[Balinus]

Optimization 1st pass include the following modifications:

Changes made

1. src/distributions/Power.jl — Direct closed-form math
   Replaced delegation through Beta(κ, 1) wrapper with direct formulas: cdf = x^κ, logpdf = log(κ) + (κ-1)log(x), quantile = p^(1/κ), rand = u^(1/κ). Also added a specialized logcdf = κ·log(x).

2. src/distributions/TruncatedNormal.jl — Cached underlying distribution
   The Truncated(Normal(...)) wrapper was being recreated on every pdf/cdf/quantile/rand call. Now precomputed once at construction and stored in a _dist field.

3. src/distributions/TruncatedBeta.jl — Same caching strategy
   The LocationScale(Truncated(Beta(...))) triple-nested wrapper is now built once at construction.

4. src/distributions/ExtendedGeneralizedPareto.jl — @inline hints + logcdf
   Added @inline on hot methods and a specialized logcdf that avoids log(cdf(...)).

5. src/parameterestimation.jl — Allocation-free hot loop

Replaced sum(logpdf.(pd, y⁺)) (allocates temp array) with an explicit @inbounds loop
Avoids constructing EGP in the uncensored path — uses V and G directly
Replaced count(y .< threshold) (allocates BitArray) with count(v -> v < threshold, y)
Used expm1(ν) for better numerics

Category	Benchmark	Speedup
quantile	EGP_Power_vector	94% faster
rand	EGP_Power_1000	95% faster
quantile	EGP_Power_scalar	86% faster
rand	EGP_Power_single	89% faster
cdf	EGP_Power_scalar	78% faster
cdf	EGP_TNormal_scalar	74% faster
fit_mle	EGP_TNormal_n500	74% faster
cdf	EGP_Power_vector	72% faster
rand	EGP_TNormal_single	71% faster
pdf	TBeta variants	60-63% faster
fit_mle	Power variants	57-59% faster
workflow	pcp_fit_and_quantile	56% faster (2.1s → 0.9s)
logpdf	all variants	29-58% faster

Construction of TNormal/TBeta is slower (they now precompute the cached distribution), but this is amortized away by the dramatic speedups on all subsequent operations.

Optimization 2nd pass - MVector include the following changes:

Changes made

1. src/parameterestimation.jl — MVector + fused GP computation

MVector{3} for Optim.jl: The optimizer initial point is now MVector(ν₀, ϕ₀, ξ₀) instead of [ν₀, ϕ₀, ξ₀]. The fixed size lets the compiler unroll simplex operations and avoids dynamic-size array overhead. (SVector isn't compatible with Optim v1.13.3's use of fill!.)
_gp_cdf_logpdf fused helper: Both cdf(GP, x) and logpdf(GP, x) internally compute z = 1 + ξ·x/σ and log(z). The new helper computes both in a single pass, eliminating the redundant computation per data point per optimizer iteration.
log(σ) = ϕ identity: Since σ = exp(ϕ), we skip computing log(σ) entirely.
Allocations dropped from 1,420 → 588 (58% fewer) and 34.2 KiB → 19.2 KiB (44% less memory).

2. src/distributions/TruncatedNormal.jl & TruncatedBeta.jl — added logcdf delegates

3. src/ExtendedExtremes.jl — added StaticArrays dependency

Results vs previous round (additional speedups)

Benchmark	Additional improvement
fit_mle EGP_TNormal_n500	-47% faster
fit_mle EGP_Power_censored_n500	-44% faster
fit_mle EGP_Power_n2000	-43% faster
fit_mle EGP_Power_n500	-42% faster
workflow pcp_fit_and_quantile	-41% faster
logpdf EGP_TNormal_vector	-20% faster

Cumulative results vs original code

Benchmark	Total speedup
fit_mle EGP_TNormal_n500	86% faster (77ms → 11ms)
fit_mle EGP_Power_n500	76% faster (66ms → 16ms)
fit_mle EGP_Power_censored	77% faster (50ms → 12ms)
workflow pcp_fit_and_quantile	74% faster (2.1s → 0.55s)
rand EGP_Power_1000	95% faster
quantile EGP_Power_vector	94% faster