Capability index

Every public name in xtremax (202 of them), each listed once at its subpackage home and grouped by the module that defines it, with the first sentence of its docstring. import xtremax re-exports the five EVT distribution classes and every name in xtremax.primitives; the point-process wrappers in xtremax.point_processes.distributions share their names with the operators they wrap. Search this page before writing a helper: if what you need is here, compose it; if it is almost here, extend it where it lives. Regenerate with make capabilities after changing a public API (tests/test_capabilities.py checks it is current).

xtremax.distributions

Name	Kind	What it does
FrechetType2GEVD	class	Fréchet Type II Generalized Extreme Value Distribution for NumPyro.
GeneralizedExtremeValueDistribution	class	Generalized Extreme Value Distribution (GEVD) for NumPyro.
GeneralizedParetoDistribution	class	Generalized Pareto Distribution (GPD) for NumPyro.
GumbelType1GEVD	class	Gumbel Type I Generalized Extreme Value Distribution for NumPyro.
WeibullType3GEVD	class	Weibull Type III Generalized Extreme Value Distribution for NumPyro.

xtremax.primitives

Pure-JAX primitives for the Fréchet (Type II) extreme value distribution (xtremax.primitives.frechet)

Name	Kind	What it does
frechet_cdf	function	Fréchet CDF.
frechet_icdf	function	Fréchet quantile function.
frechet_log_prob	function	Fréchet log PDF (assumes shape > 0).
frechet_mean	function	Fréchet mean (+inf when shape >= 1).
frechet_return_level	function	T-period return level.

Pure-JAX primitives for the Generalized Extreme Value distribution (xtremax.primitives.gev)

Name	Kind	What it does
gev_cdf	function	CDF of the Generalized Extreme Value distribution.
gev_icdf	function	Quantile function (inverse CDF) of the GEV distribution.
gev_log_prob	function	Log PDF of the Generalized Extreme Value distribution.
gev_log_survival	function	Log survival function \(\log S(x) = \log(1 - F(x))\) of the GEV.
gev_mean	function	Mean of the GEV distribution (+inf when \(\xi \ge 1\)).
gev_return_level	function	T-period return level: \(z_T = F^{-1}(1 - 1/T)\).
gev_survival	function	Survival function \(S(x) = 1 - F(x)\) of the GEV distribution.

Pure-JAX primitives for the Generalized Pareto Distribution (xtremax.primitives.gpd)

Name	Kind	What it does
gpd_cdf	function	CDF of the Generalized Pareto Distribution.
gpd_icdf	function	Quantile function (inverse CDF) of the GPD.
gpd_log_prob	function	Log PDF of the Generalized Pareto Distribution (loc = 0).
gpd_log_survival	function	Log survival \(\log S(x) = -\tfrac{1}{\xi}\log(1 + \xi x/\sigma)\).
gpd_mean	function	GPD mean: \(\sigma / (1 - \xi)\) for \(\xi < 1\), else +inf.
gpd_return_level	function	T-period return level: \(Q(1 - 1/T)\).
gpd_survival	function	Survival function \(S(x) = (1 + \xi x/\sigma)^{-1/\xi}\) of the GPD.

Pure-JAX primitives for the Gumbel Type I distribution (xtremax.primitives.gumbel)

Name	Kind	What it does
gumbel_cdf	function	Gumbel CDF: \(F(x) = \exp(-\exp(-z))\).
gumbel_icdf	function	Gumbel quantile: \(Q(p) = \mu - \sigma\log(-\log p)\).
gumbel_log_prob	function	Gumbel log PDF: \(-\log\sigma - z - e^{-z}\), \(z=(x-\mu)/\sigma\).
gumbel_mean	function	Gumbel mean: \(\mu + \sigma\gamma_E\).
gumbel_return_level	function	T-period return level: \(Q(1 - 1/T)\).

Pure-JAX primitives for non-stationary GEV return levels (xtremax.primitives.nonstationary)

Name	Kind	What it does
assemble_nonstationary_gev_fields	function	Build non-stationary spatio-temporal GEV parameter fields.
expected_exceedances	function	Expected number of block exceedances of a threshold.
nonstationary_return_level	function	Return level for stationary or non-stationary GEV parameter fields.
nonstationary_return_period	function	Return period associated with a threshold under (non-)stationary GEV.

Pure-JAX spatial building blocks for hierarchical extreme value models (xtremax.primitives.spatial)

Name	Kind	What it does
design_matrix	function	Prepend an intercept column to a static-covariate matrix.
pairwise_distances	function	Euclidean distance matrix between sites.
two_range_correlation	function	Two-range exponential correlation matrix with unit diagonal.

Pure-JAX primitives for the reverse Weibull (Type III) extreme value distribution (xtremax.primitives.weibull)

Name	Kind	What it does
weibull_cdf	function	Reverse-Weibull CDF.
weibull_icdf	function	Reverse-Weibull quantile function.
weibull_log_prob	function	Reverse-Weibull log PDF (assumes shape < 0).
weibull_mean	function	Reverse-Weibull mean (always finite for shape < 0).
weibull_return_level	function	T-period return level.

xtremax.extraction

xtremax.extraction.block_maxima

Name	Kind	What it does
declustered_block_maxima	function	Extract declustered block maxima by identifying independent extreme events.
r_largest_block_maxima	function	Extract r-largest order statistics from each block.
sliding_block_maxima	function	Extract block maxima using a sliding window approach.
spatial_block_maxima	function	Extract spatial block maximum values from an xarray DataArray.
temporal_block_maxima	function	Extract temporal block maximum values from an xarray DataArray.

xtremax.extraction.decluster

Name	Kind	What it does
decluster_runs	function	Decluster exceedances using the runs method.
decluster_separation	function	Decluster by enforcing minimum separation between peaks.
estimate_extremal_index	function	Estimate the extremal index (theta), a measure of clustering.

Quantile regression utilities for extremes thresholding (xtremax.extraction.quantile_regression)

Name	Kind	What it does
XarrayQuantileRegressor	class	Quantile regressor that operates on xr.DataArray inputs.
quantile_regression_threshold	function	Estimate a time-varying threshold via linear quantile regression.

Threshold selection for peaks-over-threshold (POT) analysis (xtremax.extraction.threshold)

Name	Kind	What it does
constant_threshold	function	Return a constant threshold value.
quantile_threshold	function	Calculate threshold based on a percentile of the data.
rolling_threshold	function	Calculate time-varying threshold using a rolling window.
seasonal_threshold	function	Calculate seasonal threshold (backward compatibility wrapper).
temporal_threshold	function	Calculate time-varying threshold based on temporal grouping.

xtremax.point_processes

Ergonomic adapters wrapping plain values as retention / mark callables (xtremax.point_processes._adapters)

Name	Kind	What it does
constant_mark_distribution	function	Mark distribution that ignores time and history and returns d.
constant_retention	function	Retention that always returns the same probability p.
time_varying_marks	function	Wrap a time → Distribution callable into the full signature.
time_varying_retention	function	Wrap a pure function of time into the full retention signature.

Axis-aligned rectangular domain and temporal interval for point processes (xtremax.point_processes._domain)

Name	Kind	What it does
RectangularDomain	class	Axis-aligned rectangle [lo, hi] ⊂ ℝᵈ.
TemporalDomain	class	Half-open temporal interval [t0, t1) ⊂ ℝ.

Padded event-history PyTree shared by all TPP families (xtremax.point_processes._history)

Name	Kind	What it does
EventHistory	class	Fixed-size buffer of events + optional marks.

Numerical integration utilities for temporal point processes (xtremax.point_processes._integration)

Name	Kind	What it does
cumulative_log_intensity	function	Shorthand for \(\Lambda(t) = \int_0^t \lambda(s) ds\).
integrate_log_intensity	function	Compute \(\int_{t_0}^{t_1} \exp(\log\lambda(s))\, ds\).

Multi-dimensional integration helpers for spatial point processes (xtremax.point_processes._integration_spatial)

Name	Kind	What it does
integrate_log_intensity_spatial	function	Compute \(\int_D \exp(\log\lambda(s))\, ds\).

Quadrature over a space-time slab D × [t0, t1) (xtremax.point_processes._integration_spatiotemporal)

Name	Kind	What it does
integrate_log_intensity_spatiotemporal	function	Compute \(\int_{t_0}^{t_1} \int_D \exp(\log\lambda(s, t))\, ds\, dt\).

Shared result types for point-process samplers and diagnostics (xtremax.point_processes._results)

Name	Kind	What it does
GoodnessOfFit	class	Bundle of diagnostics returned by goodness_of_fit.
MarkedSampleResult	class	Marked temporal sample: (times, mask, marks).
MarkedSpatialSampleResult	class	Marked spatial sample: (locations, mask, marks).
MarkedSpatiotemporalSampleResult	class	Marked spatiotemporal sample: (locations, times, mask, marks).
SampleResult	class	Unmarked temporal sample: (times, mask, n_events).
SpatialSampleResult	class	Unmarked spatial sample: (locations, mask, n_events).
SpatiotemporalSampleResult	class	Unmarked spatiotemporal sample: (locations, times, mask, n_events).

xtremax.point_processes.primitives

Goodness-of-fit diagnostics for temporal point processes (xtremax.point_processes.primitives.diagnostics)

Name	Kind	What it does
compensator_curve	function	Pairs (t_i, Λ(t_i)) for a compensator plot.
ks_statistic_exp1	function	Two-sided Kolmogorov–Smirnov statistic against Exp(1).
qq_exp1_quantiles	function	Theoretical vs empirical quantiles against Exp(1) for a QQ plot.
time_rescaling_residuals	function	Rescaled inter-event times under the compensator.

Analytical second-order summaries for spatial point processes (xtremax.point_processes.primitives.diagnostics_spatial)

Name	Kind	What it does
csr_l_function	function	Besag's L-function, the variance-stabilised K.
csr_pair_correlation	function	Pair correlation function under CSR: g(r) ≡ 1.
csr_ripleys_k	function	Theoretical Ripley's K-function under CSR, \(K(r) = V_d r^d\).
unit_ball_volume	function	Volume of the unit ℝᵈ ball: \(V_d = \pi^{d/2}/\Gamma(d/2+1)\).

Pure primitives for self-exciting (Hawkes) temporal point processes (xtremax.point_processes.primitives.hawkes)

Name	Kind	What it does
exp_hawkes_cumulative_intensity	function	Exponential-kernel Hawkes compensator.
exp_hawkes_intensity	function	Conditional intensity of the exponential-kernel Hawkes process.
exp_hawkes_lambda_max	function	Upper bound \(\mu + \alpha \cdot N(t)\) valid from the last event onward.
exp_hawkes_log_prob	function	Log-likelihood \(\sum_i \log \lambda^*(t_i) - \Lambda(T)\) for exp Hawkes.
exp_hawkes_sample	function	Ogata thinning sample of an exponential-kernel Hawkes process.
general_hawkes_cumulative_intensity	function	Compensator \(\mu T + \sum_i \int_{t_i}^{T} \phi(s - t_i) ds\).
general_hawkes_intensity	function	Conditional intensity for a general kernel.
general_hawkes_log_prob	function	Log-likelihood for a general-kernel Hawkes process.
general_hawkes_sample	function	Ogata thinning for a general-kernel Hawkes process.

Self-exciting spatiotemporal point process (ETAS-style Hawkes) (xtremax.point_processes.primitives.hawkes_spatiotemporal)

Name	Kind	What it does
stpp_hawkes_compensator	function	Closed-form compensator \(\Lambda\) of the ETAS Hawkes process.
stpp_hawkes_intensity	function	Conditional intensity \(\lambda^*(s, t)\) of the ETAS Hawkes process.
stpp_hawkes_lambda_max	function	Adaptive upper bound \(\bar\lambda = \mu + N \alpha \beta k_s(0)\).
stpp_hawkes_log_prob	function	Log-likelihood \(\sum_i \log \lambda^*(s_i, t_i) - \Lambda\).
stpp_hawkes_sample	function	Ogata-style spatiotemporal thinning sample.

Pure-JAX primitives for the Homogeneous Poisson Process on [0, T] (xtremax.point_processes.primitives.hpp)

Name	Kind	What it does
hpp_cumulative_intensity	function	Compensator \(\Lambda(t) = \lambda t\).
hpp_exceedance_log_prob	function	log P(N > k) over [start, end], computed via the Poisson CDF.
hpp_hazard	function	Constant hazard equal to rate.
hpp_intensity	function	Constant intensity \(\lambda(t) = \lambda\).
hpp_inter_event_log_prob	function	Log density of τ ~ Exp(λ): \(\log \lambda - \lambda \tau\).
hpp_log_prob	function	Log-likelihood \(\log L = n \log \lambda - \lambda T\).
hpp_mean_residual_life	function	Memorylessness gives \(\mathbb{E}[T - s \mid T > s] = 1/\lambda\).
hpp_predict_count	function	Expected event count on [start, end]: λ (end - start).
hpp_return_period	function	Time τ such that \(P(\text{no event in } \tau) = 1 - p\).
hpp_sample	function	Sample ordered event times from a homogeneous Poisson process.
hpp_survival	function	\(S(t\vert s) = \exp(-\lambda (t - s))\) for t >= s.

Pure-JAX primitives for the homogeneous spatial Poisson process (xtremax.point_processes.primitives.hpp_spatial)

Name	Kind	What it does
hpp_spatial_count_log_prob	function	Marginal Poisson-count log-pmf log P(N = n).
hpp_spatial_intensity	function	Constant intensity λ(s) = λ, broadcast against locations.
hpp_spatial_log_prob	function	Joint Janossy log-likelihood of a homogeneous Poisson pattern.
hpp_spatial_nearest_neighbor_distance	function	Expected nearest-neighbour distance for a CSR pattern in ℝᵈ.
hpp_spatial_predict_count	function	Mean and variance of the count in a sub-domain (both λ \|A\|).
hpp_spatial_sample	function	Sample a CSR realisation on a rectangular domain.

Pure-JAX primitives for the homogeneous spatiotemporal Poisson process (xtremax.point_processes.primitives.hpp_spatiotemporal)

Name	Kind	What it does
hpp_spatiotemporal_count_log_prob	function	Marginal Poisson-count log-pmf log P(N = n) with mean λ \|D\| T.
hpp_spatiotemporal_intensity	function	Constant intensity λ(s, t) = λ, broadcast against times.
hpp_spatiotemporal_log_prob	function	Janossy log-likelihood n log λ − λ \|D\| (t1 − t0).
hpp_spatiotemporal_predict_count	function	Mean and variance of the count in a sub-slab (both λ \|A\| τ).
hpp_spatiotemporal_sample	function	Sample a homogeneous spatiotemporal Poisson realisation.

Pure-JAX primitives for the Inhomogeneous Poisson Process on [0, T] (xtremax.point_processes.primitives.ipp)

Name	Kind	What it does
ipp_cumulative_hazard	function	\(\Lambda(t) - \Lambda(s)\) via quadrature.
ipp_cumulative_intensity	function	Compensator \(\Lambda(t)\) via composite trapezoid.
ipp_hazard	function	Hazard equals the intensity for an IPP.
ipp_intensity	function	Pointwise intensity λ(t) = exp(log_intensity_fn(t)).
ipp_inter_event_log_prob	function	Log density of the next-event delay τ given last event at s.
ipp_log_prob	function	Log-likelihood of an observed IPP event sequence.
ipp_predict_count	function	Expected count \(\Lambda(end) - \Lambda(start)\) on [start, end].
ipp_sample_inversion	function	Exact inversion sampling when \(\Lambda^{-1}\) is available.
ipp_sample_thinning	function	Sample via Lewis–Shedler thinning with a static buffer.
ipp_survival	function	\(S(t\vert s) = \exp(-[\Lambda(t) - \Lambda(s)])\) for t >= s.

Pure-JAX primitives for the inhomogeneous spatial Poisson process (xtremax.point_processes.primitives.ipp_spatial)

Name	Kind	What it does
ipp_spatial_intensity	function	Pointwise intensity λ(s) = exp(log_intensity_fn(s)).
ipp_spatial_log_prob	function	Log-likelihood of an observed inhomogeneous spatial pattern.
ipp_spatial_predict_count	function	Expected count over a sub-domain A.
ipp_spatial_sample_thinning	function	Lewis–Shedler thinning sampler with a static buffer.

Pure-JAX primitives for the inhomogeneous spatiotemporal Poisson process (xtremax.point_processes.primitives.ipp_spatiotemporal)

Name	Kind	What it does
ipp_spatiotemporal_chi_square_gof	function	Pearson \(\chi^2\) statistic from binned residuals.
ipp_spatiotemporal_intensity	function	Evaluate λ(s, t) = exp(log λ(s, t)) on a batch of events.
ipp_spatiotemporal_intensity_surface_at_time	function	Evaluate λ(s, t) on a tensor-product spatial grid at fixed t.
ipp_spatiotemporal_log_prob	function	Janossy log-likelihood \(\sum_i \log \lambda(s_i, t_i) - \Lambda\).
ipp_spatiotemporal_marginal_spatial_intensity	function	Compute \(\lambda_S(s) = \int_{t_0}^{t_1} \lambda(s, t)\, dt\).
ipp_spatiotemporal_marginal_temporal_intensity	function	Compute \(\lambda_T(t) = \int_D \lambda(s, t)\, ds\).
ipp_spatiotemporal_pearson_residuals	function	Pearson residuals on a tensor-product space-time grid.
ipp_spatiotemporal_predict_count	function	Mean and variance of the Poisson count over the integration domain.
ipp_spatiotemporal_sample_thinning	function	Lewis–Shedler thinning on D × [t_0, t_1).

Primitives for marked temporal point processes (xtremax.point_processes.primitives.marked)

Name	Kind	What it does
marks_log_prob	function	Sum of log f(mᵢ \| tᵢ, Hᵢ) over real events.
sample_marks_at_times	function	Draw marks mᵢ ~ f(· \| tᵢ, Hᵢ) at each observed time.

Primitives for marked spatial point processes (xtremax.point_processes.primitives.marked_spatial)

Name	Kind	What it does
sample_spatial_marks_at_locations	function	Draw marks mᵢ ~ f(· \| sᵢ) at every location.
spatial_marks_log_prob	function	Sum of log f(mᵢ \| sᵢ) over real events.

Primitives for marked spatiotemporal point processes (xtremax.point_processes.primitives.marked_spatiotemporal)

Name	Kind	What it does
sample_spatiotemporal_marks	function	Draw marks \(m_i \sim f(\cdot \mid s_i, t_i)\) at every event.
spatiotemporal_marks_log_prob	function	Sum of \(\log f(m_i \mid s_i, t_i)\) over real events.

Pure primitives for 1-D renewal temporal point processes (xtremax.point_processes.primitives.renewal)

Name	Kind	What it does
renewal_cumulative_hazard	function	\(\Lambda(\tau) = -\log S(\tau) = -\log(1 - F(\tau))\).
renewal_expected_count	function	Expected number of events on [0, T] via the renewal equation.
renewal_hazard	function	Hazard of the inter-event distribution: \(h(\tau) = f(\tau)/S(\tau)\).
renewal_intensity	function	Conditional intensity \(\lambda^*(t) = h(t - t_{N(t)})\).
renewal_inter_event_log_prob	function	Log density of an inter-event gap: log f(τ).
renewal_log_prob	function	Log-likelihood of an observed renewal-process sequence.
renewal_ogata_intensity_fn	function	Build a (t, history) -> λ*(t) closure usable by thinning samplers.
renewal_sample	function	Sample a renewal-process event sequence by accumulating gaps.
renewal_survival	function	S(τ) = 1 − F(τ) clipped to be non-negative.

Generic Ogata thinning sampler and retention primitives (xtremax.point_processes.primitives.thinning)

Name	Kind	What it does
retention_compensator	function	Compute the retention compensator via trapezoid quadrature.
thinning_retention_log_prob	function	Sum of log p(tᵢ \| Hᵢ, mᵢ) over retained events.
thinning_sample	function	Sample a history-dependent temporal point process via Ogata thinning.

xtremax.point_processes.operators

Name	Kind	What it does
ExponentialHawkes	class	Hawkes process with exponential excitation on [0, T].
ExponentialKernel	class	Exponential excitation kernel \(\phi(\tau) = \alpha e^{-\beta \tau}\).
GeneralHawkesProcess	class	Hawkes process with a user-supplied kernel module.
HomogeneousPoissonProcess	class	Homogeneous Poisson process on [0, T].
HomogeneousSpatialPP	class	Homogeneous spatial Poisson process on a rectangular domain.
HomogeneousSpatioTemporalPP	class	Homogeneous Poisson process on D × [t0, t1).
InhomogeneousPoissonProcess	class	Inhomogeneous Poisson process on [0, T].
InhomogeneousSpatialPP	class	Inhomogeneous spatial Poisson process on a rectangular domain.
InhomogeneousSpatioTemporalPP	class	Inhomogeneous Poisson process on D × [t0, t1).
MarkedSpatialPP	class	Separable marked spatial PP: ground process × mark distribution.
MarkedSpatioTemporalPP	class	Separable marked spatiotemporal PP: ground × mark distribution.
MarkedTemporalPointProcess	class	Separable marked TPP: ground process + time-/history-conditioned marks.
PiecewiseConstantLogIntensity	class	Piecewise-constant log-intensity as an eqx.Module.
RenewalProcess	class	Renewal process on [0, T] with a user-supplied inter-event law.
SpatioTemporalHawkes	class	ETAS-style separable exp-Gaussian Hawkes process.
ThinningProcess	class	Thinned TPP: base ground process + retention callable.

xtremax.point_processes.distributions

Name	Kind	What it does
ExponentialHawkes	class	NumPyro wrapper for an exponential-kernel Hawkes process.
GeneralHawkesProcess	class	NumPyro wrapper for a general-kernel Hawkes process.
HomogeneousPoissonProcess	class	NumPyro wrapper for a homogeneous temporal Poisson process.
HomogeneousSpatialPP	class	NumPyro wrapper for a homogeneous spatial Poisson process.
HomogeneousSpatioTemporalPP	class	NumPyro wrapper for a homogeneous spatiotemporal Poisson process.
InhomogeneousPoissonProcess	class	NumPyro wrapper for an inhomogeneous temporal Poisson process.
InhomogeneousSpatialPP	class	NumPyro wrapper for an inhomogeneous spatial Poisson process.
InhomogeneousSpatioTemporalPP	class	NumPyro wrapper for an inhomogeneous spatiotemporal Poisson process.
MarkedSpatialPP	class	NumPyro wrapper for a separable marked spatial Poisson process.
MarkedSpatioTemporalPP	class	NumPyro wrapper for a separable marked spatiotemporal Poisson process.
MarkedTemporalPointProcess	class	NumPyro wrapper for a separable marked temporal point process.
RenewalProcess	class	NumPyro wrapper for a renewal temporal point process.
SpatioTemporalHawkes	class	NumPyro wrapper for a separable exp-Gaussian spatiotemporal Hawkes process.
ThinningProcess	class	NumPyro wrapper for a thinned TPP.

xtremax.simulations

Variable-specific extreme value generators (xtremax.simulations.extremes)

Name	Kind	What it does
compute_climate_signal	function	Combines Spatial and Temporal fields to create a mean climate signal (Mu).
generate_spatial_field	function	Generates static spatial data: Lat, Lon, Elevation, Distance to Coast.
simulate_precip_extremes	function	Simulates Precipitation Extremes: 1.
simulate_temp_extremes	function	Simulates Block Maxima Temperature via the GEV distribution.
simulate_wind_extremes	function	Simulates Extreme Wind Speeds (Gusts) using Weibull distribution.

Synthetic spatial-domain generators (xtremax.simulations.spatial)

Name	Kind	What it does
SpatialFeatureExtractor	class	Static methods to derive physical features from a Digital Elevation Model (DEM).
augment_spatial_features	function	Pipeline to run all extractors and merge into Dataset.
compute_advanced_climate_signal	function	Generates Tmax and Precip Mean fields using advanced physics proxies.
create_iberian_domain	function	Creates the master spatial dataset with Lat, Lon, Elevation, and Land Mask.
generate_fractal_terrain	function	Generates coherent terrain using Fractal Brownian Motion (fBm).
generate_iberia_mask	function	Procedurally generates a boolean mask approximating the Iberian Peninsula and Balearic Islands using geometrical primitives.

Temporal GMST trajectory generators (xtremax.simulations.temporal)

Name	Kind	What it does
generate_gmst_trajectory	function	Generates a synthetic Global Mean Surface Temperature (GMST) anomaly curve.
generate_physical_gmst	function	Simulates Global Mean Surface Temperature (GMST) using a 0-D Energy Balance Model.