Package index • mathmodels

Evaluation Algorithms

Evaluation, weighting, fuzzy evaluation, DEA, inequality, regional economics, and system evaluation methods.

Data Preprocessing

Scaling, normalization, and indicator transformation utilities.

standardize() normalize() rescale() rescale_middle() rescale_interval() rescale_extreme() rescale_initial() rescale_mean() to_positive(): Preprocessing Functions for Data Normalization and Standardization

Weighting Methods

Subjective, objective, and combined weighting methods for multi-indicator evaluation.

AHP(): AHP: Analytic Hierarchy Process
combine_weights(): Combine Subjective and Objective Weights
weight_critic(): CRITIC Weight Method
weight_cv(): Coefficient of Variation Weighting
weight_entropy(): Entropy Weight Method
weight_fa(): Factor-Analysis-Based Weighting Method
linear_sum(): Linear weighted synthesis
weight_pca(): PCA-Based Weighting Method

Evaluation Models

Multi-criteria ranking and grey relational evaluation methods.

topsis(): TOPSIS Method for Multi-Criteria Decision Making
rank_sum_ratio(): Rank Sum Ratio (RSR) Evaluation
grey_corr() grey_corr_topsis(): Grey Relational Analysis Functions

Fuzzy Evaluation

Membership functions, fuzzy comprehensive evaluation, and defuzzification.

mf_tri() mf_trap() mf_gauss() mf_gbell() mf_gauss2() mf_sigmoid() mf_dsigmoid() mf_psigmoid() mf_z() mf_pi() mf_s() plot_mf(): Membership Functions for Fuzzy Logic
compute_mf_funs() compute_mf(): Build membership functions from knots
fuzzy_eval(): Fuzzy Comprehensive Evaluation
defuzzify(): Defuzzification Methods for Fuzzy Comprehensive Evaluation

Data Envelopment Analysis

DEA, SBM, super-efficiency, and Malmquist productivity models.

basic_DEA() super_DEA() basic_SBM() super_SBM() malmquist(): DEA efficiency analysis

Inequality Measures

Gini and Theil indices for individual, grouped, and nested data.

gini0() gini() theil0() theil() theil0_g() theil_g() theil_g2_cross() theil_g2_nest(): Inequality Indices

Regional Economics

Regional and industrial concentration indices.

LQ() HHI() EG(): Regional Economics Functions

System Evaluation

Coupling coordination and obstacle degree analysis for multi-indicator systems.

coupling_degree() obstacle_degree(): System Evaluation Functions for Coupling and Obstacle Analysis

Prediction Algorithms

Grey prediction, Markov prediction, regression, and time series models.

Grey Prediction Models

Grey forecasting models and utilities for combining predictions.

GM11() GM1N() DGM21() verhulst(): Grey Prediction Models
combine_preds(): Combine Multiple Prediction Results

Markov Prediction Models

Markov chain prediction and Grey-Markov forecasting models.

markov_chain(): Markov Chain Prediction
GM11_markov(): Grey-Markov Prediction Model

Time Series Models

Time series data structure, transformation, diagnostics, modeling, forecasting, and visualization.

ts_df(): Lightweight Time-Series Data Frame
as_ts_df(): Convert Common Inputs to ts_df
is_ts_df(): Check Whether an Object Is a ts_df
validate_ts_df(): Validate a ts_df
complete_ts_df(): Complete Missing Time Points
impute_ts_df(): Complete and Interpolate a ts_df
drop_na_ts_df(): Drop Missing Values from a ts_df
ts_transform(): Transform a ts_df
ts_back_transform(): Back-Transform Forecasts
ts_test(): Stationarity Tests for a Time Series
ts_stl(): STL Decomposition for a ts_df
ts_ets(): ETS Model Fitting
ts_sarima(): SARIMA Model Fitting
ts_arimax(): ARIMAX Model Fitting
ts_forecast(): Generate Forecasts
plot_ts(): Plot a Time Series
plot_ts_forecast(): Plot Forecasts
plot_ts_residuals(): Residual Diagnostic Plot
plot_ts_stl(): STL Decomposition Plot
plot_ts_acf(): Autocorrelation Plot
plot_ts_pacf(): Partial Autocorrelation Plot

Regression Prediction Models

Linear, logistic, Poisson, and negative binomial regression with stepwise selection, diagnostics, and visualization.

reg_lm(): Multivariable Linear Regression
reg_logistic(): Logistic Regression
reg_poisson(): Poisson Regression
reg_negbin(): Negative Binomial Regression
reg_diagnostics(): Model Diagnostics
reg_predict(): Predictions
plot_reg_residuals(): Residual Diagnostics
plot_reg_predict(): Prediction Plot

Multivariate Statistics

Dimension reduction, clustering, discrimination, and correlation structure analysis.

Dimension Reduction

Principal component and exploratory factor analysis.

mv_pca(): Principal Component Analysis
mv_efa(): Exploratory Factor Analysis
plot_mv_scree(): Scree Plot
plot_mv_scores(): Scores Plot

Clustering Analysis

Hierarchical clustering, k-means, validity metrics, and diagnostic plots.

mv_hclust(): Hierarchical Clustering
mv_kmeans(): K-means Clustering
mv_cluster_metrics(): Clustering Validity Metrics
plot_mv_elbow(): Elbow Plot
plot_mv_silhouette(): Silhouette Plot
plot_mv_dendrogram(): Dendrogram Plot

Discriminant Analysis

Linear and quadratic discriminant analysis.

mv_discrim(): Linear and Quadratic Discriminant Analysis

Correspondence Analysis and Scaling

Correspondence analysis and multidimensional scaling.

mv_corresp(): Simple Correspondence Analysis
mv_mds(): Multidimensional Scaling
plot_mv_corresp(): Correspondence Analysis Map
plot_mv_mds(): MDS Configuration Plot

Correlation Structure

Canonical and partial correlation analysis.

mv_cancor(): Canonical Correlation Analysis
mv_pcor(): Partial Correlation Matrix

Curve Fitting & Interpolation

Polynomial fitting, linearizable curve fitting, growth models, and interpolation methods.

poly_fit(): Polynomial Fit
curve_fit(): Linearizable Curve Fit
growth_fit(): Nonlinear Growth Curve Fit
interp_linear(): Linear Interpolation
interp_poly(): Polynomial Interpolation
interp_hermite(): Piecewise Cubic Hermite Interpolation
interp_spline(): Cubic Spline Interpolation

Differential Equation Algorithms

ODE solvers, dynamic models, epidemic models, metrics, and visualizations.

Differential Equation Models

ODE solving, population dynamics, epidemic models, metrics, and visualizations.

ode_solver(): General ODE Solver
ode_malthus(): Malthusian (Exponential) Growth Model
ode_logistic(): Logistic Population Growth Model
ode_si(): SI Epidemic Model
ode_sis(): SIS Epidemic Model
ode_sir(): SIR Epidemic Model
ode_seir(): SEIR Epidemic Model
ode_lv(): Lotka-Volterra Predator-Prey Model
epi_metrics(): Extract key epidemic metrics from ODE simulation output
plot_compartments(): Plot compartment trajectories
plot_incidence(): Plot daily new infections (dI)
plot_phase_si(): Phase plot S vs I
plot_Rt_estimate(): Plot effective reproduction number R_t

Data and Utilities

Built-in datasets and data import utilities.

Data Cleaning

Missing-value diagnostics, imputation (simple, model-based, and multiple), Rubin’s-rules pooling, and outlier handling.

na_summary(): Missing Value Summary
na_mcar_test(): Little's MCAR Test
plot_na_heatmap(): Missingness Heatmap
plot_na_bar(): Missingness Bar Plot
impute(): Simple Missing Value Imputation
impute_model(): Model-Based Missing Value Imputation
impute_multiple(): Multiple Imputation via FCS
rubin_pool(): Pool Estimates via Rubin's Rules
pool_fit(): Pool lm/glm Fits Across Imputations
outlier(): Outlier Detection and Handling
pivot_table(): Pivot Table

Statistical Inference

Tidy hypothesis tests, bootstrap and permutation frameworks, and three-line table export.

stat_describe(): Descriptive Statistics
stat_t_test(): t-test (one-sample, two-sample, Welch, paired)
stat_wilcox_test(): Wilcoxon / Mann-Whitney Tests
stat_anova(): Analysis of Variance (ANOVA)
stat_kruskal(): Kruskal-Wallis Rank Sum Test
stat_ancova(): Analysis of Covariance (ANCOVA)
stat_cor(): Correlation Analysis
stat_chisq(): Chi-square Test of Independence
stat_normality(): Normality Tests
stat_hov_test(): Variance Homogeneity Tests
stat_bootstrap(): Bootstrap Estimation and Confidence Intervals
stat_perm_test(): Permutation Test
export_table(): Three-line Table Export (Word / LaTeX)

Datasets

water_quality: Water Quality Dataset

Data I/O Utilities

read_nbs(): Read and Combine National Bureau of Statistics XLS Files