Package index • corehydror

Distributions

The general univariate distribution interface: 38 families with density, quantile, seeded random generation, and fitting.

distribution(): Create a univariate distribution object
dist_pdf() dist_log_pdf() dist_cdf() dist_quantile() dist_random(): Distribution functions
dist_moments() dist_params() dist_lmoments() dist_log_likelihood(): Distribution properties
dist_fit(): Fit a distribution to data
distribution_names(): List the supported distribution families

Composite distributions

Five distributions built from other distributions rather than a flat parameter vector – truncation, mixtures, competing risks, empirical, and kernel density. Each returns a corehydro_dist accepted by every dist_*() verb.

dist_truncated(): Truncate a distribution
dist_mixture(): Mixture distribution
dist_competing_risks(): Competing-risks distribution
dist_empirical(): Empirical distribution
dist_kde(): Kernel density distribution

Copulas

The seven bivariate copula families (copula_names()), constructed directly or fitted to paired data.

copula(): Construct a bivariate copula
copula_fit(): Fit a bivariate copula to data
copula_pdf() copula_log_pdf() copula_cdf(): Copula density, distribution, and inverse functions
copula_inverse_cdf(): Copula inverse CDF
copula_tail_dependence(): Copula tail dependence
copula_exceedance(): Copula joint exceedance probability
copula_bounds(): Copula theta bounds
copula_params(): Copula parameters
copula_random(): Draw from a copula
copula_log_likelihood(): Copula log-likelihood
copula_names(): List the supported copula families

Multivariate distributions

The five multivariate distribution families (mvdist_names()): multivariate normal and Student-t, Dirichlet, multinomial, and bivariate empirical.

mvdist_normal(): Construct a multivariate normal distribution
mvdist_student_t(): Construct a multivariate Student-t distribution
mvdist_dirichlet(): Construct a Dirichlet distribution
mvdist_multinomial(): Construct a multinomial distribution
mvdist_bivariate_empirical(): Construct a bivariate empirical distribution
mvdist_pdf() mvdist_log_pdf() mvdist_cdf() mvdist_dimension(): Multivariate density, distribution, and dimension
mvdist_mean() mvdist_variance() mvdist_sd() mvdist_median() mvdist_mode() mvdist_covariance(): Multivariate moments
mvdist_mahalanobis(): Mahalanobis distance
mvdist_inverse_cdf(): Multivariate inverse CDF (Cholesky map)
mvdist_interval(): Rectangle probability of a multivariate normal
mvdist_marginal(): Marginal distribution of a multivariate normal
mvdist_conditional(): Conditional distribution of a multivariate normal
mvdist_random(): Draw from a multivariate distribution
mvdist_params(): Family-specific multivariate parameters
mvdist_names(): List the supported multivariate distribution families

GEV convenience functions

dgev() pgev() qgev(): Generalized Extreme Value distribution
gev_fit(): Fit a GEV distribution
gev_moments(): Moments of a GEV distribution
gev_quantile_se(): Standard error of a GEV quantile (maximum likelihood)

Observation data

Censored observation frames – historical and paleoflood intervals, perception thresholds, measurement uncertainty, and low outliers – plus the diagnostics computed off them.

analysis_data(): Censored observation data for an analysis
analysis_data_summary(): Summarize an observation frame
analysis_data_hypothesis_test(): A hypothesis test on an observation record
analysis_data_statistics(): Summary statistics for an observation record
threshold_diagnostics(): Threshold selection diagnostics for peaks-over-threshold analysis

Models

The nine RMC.BestFit model families as plain specs, with nonstationary trends and per-parameter bounds and priors. Pass one to any analysis in place of a data vector.

model_univariate(): Univariate distribution model
model_mixture(): Finite mixture model
model_competing_risks(): Competing risks model
model_point_process(): Peaks-over-threshold point process model
model_bulletin17c(): Bulletin 17C distribution model
model_ar(): Autoregressive AR(p) model
model_ma(): Moving-average MA(q) model
model_arima(): ARIMA(p, d, q) model
model_arimax(): ARIMAX(p, d, q, b) model with covariates
model_spatial_gev(): Hierarchical spatial GEV model
model_rating_curve(): BaRatin stage-discharge rating curve model
model_bivariate(): Bivariate copula model
trend(): Attach a trend to a distribution parameter
model_parameter(): Constrain or prime one model parameter
model_validate(): Validate a model
model_simulate(): Simulate from a model
model_log_likelihood(): Model log-likelihood
model_parameters(): Model parameters

Point-estimate fits

fit_mle(): Maximum likelihood fit
fit_map(): Maximum a posteriori fit

Bayesian and GMM fits

fit_bayesian(): Bayesian MCMC fit
fit_gmm(): Generalized method of moments fit (Bulletin 17C)
fit_gmm_moments(): Fit your own moment conditions by GMM
fit_diagnostics(): Estimation diagnostics for a fit
quantile_variance(): Delta-method variance of a fitted quantile

Fit accessor methods

S3 methods on a corehydro_fit (from fit_mle, fit_map, fit_bayesian or fit_gmm). print, summary, coef and vcov are undocumented plain methods and don’t appear here.

logLik(<corehydro_fit>): Log-likelihood of a fit
confint(<corehydro_fit>): Confidence or credible intervals for a fit

Frequency analysis

univariate_analysis(): Bayesian univariate frequency analysis
fit_distributions(): Fit and rank candidate distributions
bulletin17c_analysis(): Bulletin 17C flood-frequency analysis
composite_analysis(): Composite frequency analysis

Model-family analyses

mixture_analysis(): Bayesian mixture-model frequency analysis
competing_risk_analysis(): Bayesian competing-risk frequency analysis
point_process_analysis(): Bayesian point-process (peaks-over-threshold) frequency analysis
spatial_gev_analysis(): Hierarchical spatial-GEV frequency analysis
bivariate_analysis(): Bivariate (copula) joint-exceedance frequency analysis
coincident_frequency_analysis(): Coincident-frequency analysis
rating_curve_analysis(): Stage-discharge rating-curve frequency analysis

Time series

ar_analysis(): Bayesian autoregressive AR(p) time-series analysis
ma_analysis(): Bayesian moving-average MA(q) time-series analysis
arima_analysis(): Bayesian ARIMA(p,d,q) time-series analysis
arimax_analysis(): Bayesian ARIMAX(p,d,q) time-series analysis

MCMC

mcmc_sample(): Sample the posterior of a distribution's parameters by MCMC
mcmc_posterior(): Sample your own posterior by MCMC

Uncertainty and diagnostics

bootstrap_analysis(): Parametric bootstrap confidence bands for a distribution
bootstrap_custom(): Bootstrap your own statistic
estimation_diagnostics(): Bayesian estimation diagnostics (leverage / influence / prior influence)
prior_predictive_check(): Prior predictive check
posterior_predictive_check(): Posterior predictive check

Statistics utilities

mgbt_test(): Multiple Grubbs-Beck low-outlier test
box_cox_lambda() box_cox() box_cox_inverse(): Box-Cox transformation
yeo_johnson_lambda() yeo_johnson() yeo_johnson_inverse(): Yeo-Johnson transformation
plotting_positions(): Plotting positions
latin_hypercube(): Latin hypercube sampling

Correlation and goodness of fit

Correlation coefficients and the GoodnessOfFit metrics (continuous and binary classification), plus the information criteria and model-weight verbs used to rank candidate fits.

correlation(): Correlation between two samples, or a correlation matrix
goodness_of_fit(): Goodness-of-fit metrics for a modeled series
classification_metrics(): Classification metrics for two binary label vectors
gof_test(): Goodness-of-fit test statistic for a fitted distribution
gof_rmse(): Root mean squared error of a fitted distribution
aic() aicc() bic(): Information criteria
aic_weights() rmse_weights(): Model weights from a vector of criteria

Statistics

Sample moments, L-moments, ranks and percentiles, running (online) statistics and covariance, autocorrelation and cross-correlation, and the discrete Fourier transform.

summary_statistics(): Summary statistics for a sample
product_moments(): Product moments of a sample
l_moments(): L-moments of a sample
ranks(): Ranks of a sample
percentile(): Percentiles of a sample
running_statistics(): Streaming summary statistics
running_covariance(): Streaming covariance and correlation matrix
autocorrelation(): Autocorrelation, autocovariance, or partial autocorrelation function
cross_correlation(): Cross-correlation of two series
dft(): Discrete Fourier transform
dft_real(): Discrete Fourier transform of real-valued data

Hypothesis tests

The twelve ported Numerics one- and two-sample parametric and nonparametric hypothesis tests (t-tests, the F-test and its two-model form, Jarque-Bera, Wald-Wolfowitz, Ljung-Box, Mann-Whitney, Mann-Kendall, the linear trend test).

hypothesis_test(): Hypothesis tests

Interpolation and regression

Histogram binning, one- and two-dimensional interpolation with optional axis transforms, and ordinary least squares regression.

histogram(): Bin a sample into a histogram
interpolate(): Interpolate a paired series
interpolate_2d(): Interpolate a 2D grid (bilinear interpolation)
linear_regression(): Ordinary least squares by singular value decomposition
predict(<corehydro_lm>): Predict from a fitted linear regression

Sampling utilities

Quasi-random Sobol sequences, deterministic stratification of an interval, and joint exceedance probabilities under a dependency structure.

sobol_sequence(): Sobol quasi-random low-discrepancy sequence
stratify(): Stratify an axis into equal-width bins
joint_probability(): Joint probability of multiple events

Links and trends

The Numerics link-function layer (identity, log, logit, and friends) and the trend models used by nonstationary distributions and models.

link_function(): Construct a link function
link() link_inverse() link_derivative(): Evaluate a link function
link_names(): Available link function types
trend_predict() trend_parameters(): Evaluate a trend model
trend_names(): Available trend model types

Optimizers and network routing

The fourteen ported Numerics optimizers (differential evolution, particle swarm, shuffled complex evolution, simulated annealing, multi-start, MLSL, BFGS, Powell, ADAM, gradient descent, Nelder-Mead, Brent, golden section, augmented Lagrange) over a user-written R objective, and the Dijkstra shortest-path solver from the same upstream Optimization namespace.

optim_minimize() optim_maximize(): Minimize or maximize a user-written objective
optim_constraint(): Declare one constraint for the augmented Lagrange optimizer
shortest_path(): Shortest paths through a network

Root finding, integration and differentiation

The ported Numerics Brent root finder, adaptive Gauss-Kronrod integrator and NumericalDerivative routines over a user-written R function.

root_find(): Find a root of a user-written function
root_find_system(): Solve a system of nonlinear equations
quadrature(): Integrate a user-written function
quadrature_2d(): Integrate a user-written function of two variables over a rectangle
quadrature_nd(): Integrate a user-written function over a multidimensional box
ode_solve(): Solve a user-written ordinary differential equation
derivative() gradient() hessian(): Differentiate a user-written function

Linear algebra and special functions

The ported Numerics QRDecomposition (Householder reflections) and GaussJordanElimination linear-algebra routines, the Debye and Evaluate special functions, and the two non-tabular IUnivariateFunction implementations (LinearFunction, PowerFunction).

qr_decomposition(): QR decomposition
qr_solve(): Solve a linear system by QR decomposition
gauss_jordan(): Gauss-Jordan elimination
debye(): The Debye function
polynomial_eval(): Evaluate a polynomial
univariate_function(): Evaluate a univariate function

Paired-data curves

The ported Paired Data subsystem (OrderedPairedData, UncertainOrderedPairedData) and its third IUnivariateFunction implementation, TabularFunction: interpolation and area under a curve, three simplification algorithms, sampling an uncertain curve at its mean or a quantile, and evaluating a tabular function built from that curve.

curve_interpolate(): Interpolate a paired x-y curve
curve_area(): Area under a paired x-y curve
curve_simplify(): Simplify a paired x-y curve
uncertain_curve_sample(): Sample an uncertain paired curve
tabular_function(): Evaluate a tabular function

Machine learning

The ported Numerics.MachineLearning layer: three unsupervised methods (k-means, Gaussian mixture models, Jenks natural breaks) and five supervised ones (decision trees, random forests, k-nearest neighbors, Gaussian naive Bayes, and generalized linear models). Each trains and answers in one call; a seeded fit is reproducible and agrees bit for bit with the identical call in Python.

ml_kmeans(): k-means clustering
ml_gaussian_mixture(): Gaussian mixture model
ml_jenks_breaks(): Jenks natural breaks classification
ml_decision_tree(): Decision tree regression or classification
ml_random_forest(): Random forest regression or classification
ml_knn(): k-nearest-neighbors regression or classification
ml_naive_bayes(): Gaussian naive Bayes classification
ml_glm(): Generalized linear model

Time-series container

The ported Numerics TimeSeries container. A time_series() carries dated observations on a stated interval; the verbs over it smooth, fill, clip, re-interval, summarize, reduce to annual maxima or peaks over a threshold, decompose, and resample. Seeded resampling agrees bit for bit with the identical call in Python.

time_series(): Create a time series
ts_interval_names(): The time intervals a time series can carry
ts_moving_average() ts_moving_sum(): Moving average and moving sum
ts_cumulative_sum() ts_difference() ts_standardize(): Cumulative sum, successive differences and standardization
ts_sort(): Sort a time series
ts_transform(): Transform the values of a time series
ts_replace_missing() ts_interpolate_missing() ts_fill_missing_dates(): Handle missing values
ts_clip() ts_shift() ts_convert_interval(): Clip, shift and re-interval a time series
ts_statistics() ts_hypothesis_test() ts_percentiles() ts_duration(): Summary statistics of a time series
ts_monthly_statistics() ts_monthly_percentiles() ts_monthly_frequency(): Monthly statistics
ts_block_series() ts_water_year() ts_calendar_year(): Block series: annual maxima and other block extremes
ts_peaks_over_threshold(): Peaks over a threshold
ts_seasonal_decompose(): Seasonal decomposition
ts_resample_knn() ts_resample_block_bootstrap(): Resample a time series

The generator a callback is handed

Drawing from the core’s seeded random number generator inside a function you write, so the run stays reproducible and agrees with the identical run in Python.

rng_uniform() rng_integers(): Draw from the generator a callback is handed