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
critic_weight(): CRITIC Weight Method
cv_weight(): Coefficient of Variation Weighting
entropy_weight(): Entropy Weight Method
linear_sum(): Linear weighted synthesis
pca_weight(): 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.

tri_mf() trap_mf() gauss_mf() gbell_mf() gauss2mf() sigmoid_mf() dsigmoid_mf() psigmoid_mf() z_mf() pi_mf() s_mf() 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

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
model_malthus(): Malthusian (Exponential) Growth Model
model_logistic(): Logistic Population Growth Model
model_si(): SI Epidemic Model
model_sis(): SIS Epidemic Model
model_sir(): SIR Epidemic Model
model_seir(): SEIR Epidemic Model
model_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.

Datasets

water_quality: Water Quality Dataset

Data I/O Utilities

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