Worked Examples

Example 1: Median sliding-block EVI fit

import numpy as np
from unibm import estimate_evi_quantile, estimate_design_life_level
from unibm.evi import estimate_design_life_level_interval

sample = np.random.default_rng(7).pareto(2.0, 4096) + 1.0
fit = estimate_evi_quantile(sample, quantile=0.5, sliding=True, bootstrap_reps=120)
design_life = estimate_design_life_level(
    fit,
    years=np.array([10.0, 50.0]),
    observations_per_year=365.25,
)
design_life_interval = estimate_design_life_level_interval(
    fit,
    years=np.array([10.0, 50.0]),
    observations_per_year=365.25,
)

Read fit.slope as the headline xi estimate, fit.confidence_interval for uncertainty, and fit.plateau_bounds for the selected regression window. design_life contains the resulting design-life-level estimates on the original data scale, while design_life_interval returns the matching conditional interval bounds from the fitted coefficient covariance.

Example 2: Bootstrap covariance backbone

import numpy as np
from unibm.evi import generate_block_sizes
from unibm.evi.bootstrap import (
    build_block_summary_bootstrap_backbone,
    evaluate_block_summary_bootstrap_backbone,
)

sample = np.random.default_rng(13).pareto(2.0, 4096) + 1.0
block_sizes = generate_block_sizes(sample.size)
backbone = build_block_summary_bootstrap_backbone(sample, block_sizes, sliding=True, reps=64)
quantile_boot = evaluate_block_summary_bootstrap_backbone(backbone, target="quantile")

The most useful outputs here are quantile_boot["block_sizes"], quantile_boot["samples"], and quantile_boot["covariance"]. They feed covariance-aware EVI fits without redoing the resampling step.

Example 3: Pooled extremal-index fit

import numpy as np
from unibm.ei.preparation import prepare_ei_bundle
from unibm.ei.bm import estimate_pooled_bm_ei

sample = np.random.default_rng(21).pareto(2.0, 4096) + 1.0
bundle = prepare_ei_bundle(sample)
fit = estimate_pooled_bm_ei(bundle, base_path="bb", sliding=True, regression="OLS")

Read fit.theta_hat as the headline EI estimate and fit.confidence_interval for its uncertainty. fit.stable_window shows which block-size region was pooled. If you later supply a bootstrap covariance result and switch to regression="FGLS", the observed path is still what gets pooled; the bootstrap only supplies the covariance weights.