Description
Five Novel Stochastic Regression Models with Arvind-Distributed Errors and Effects.
Description
Implements the 'Arvind' distribution and five novel stochastic regression models that replace the traditional Gaussian error assumption with 'Arvind'-distributed errors. The 'Arvind' distribution is a flexible single-parameter continuous distribution on the positive real line characterised by a polynomial numerator with Gaussian-type decay. The package provides complete distribution functions (darvind(), parvind(), qarvind(), rarvind()), maximum likelihood estimation via fit_arvind_mle(), and five model-fitting routines: Random Walk on Coefficients via fit_rw1(), Time-Varying Coefficient Linear Model via fit_tvlm(), Simulation-Extrapolation via fit_simex(), Mixed-Effects Regression via fit_mixed(), and Regime-Switching Hidden Markov Model via fit_hmm(). Additionally provides Monte Carlo forecasting with prediction intervals via forecast_arvind(), comprehensive goodness-of-fit diagnostics (21 metrics and 25 plots) via diagnostics_arvind() and plot_arvind(), k-fold and rolling-window cross-validation via cv_arvind(), and unified model comparison via summary_arvind(). For more details see Pandey, Singh, Tyagi, and Tyagi (2024) "Modelling climate, COVID-19, and reliability data: A new continuous lifetime model under different methods of estimation", Statistics and Applications, 22(2), <https://ssca.org.in/journal.html>.
README.md
ArvindSt
ArvindSt is an R package implementing the Arvind distribution and five novel stochastic regression models with Arvind-distributed errors.
Installation
Install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("shikhartyagi/ArvindSt")
Features
- Distribution Functions:
darvind(),parvind(),qarvind(),rarvind(),rarvind_centred() - Five Regression Models:
fit_rw1()— Random Walk on Coefficientsfit_tvlm()— Time-Varying Coefficient Linear Modelfit_simex()— Simulation-Extrapolationfit_mixed()— Mixed-Effects Regressionfit_hmm()— Regime-Switching (HMM)
- Diagnostics:
diagnostics_arvind()(21 metrics),plot_arvind()(25 plots) - Forecasting:
forecast_arvind()with Monte Carlo prediction intervals - Cross-Validation:
cv_arvind()(k-fold and rolling-window) - Model Comparison:
summary_arvind()
Quick Start
library(ArvindSt)
# Load example data
data(climate_consumption)
# Define formula
frm <- Consumption ~ Precip + TempMaxAvg + TempMinAvg + HumidMax + HumidAvg
# Fit all five models
m1 <- fit_rw1(frm, climate_consumption)
m2 <- fit_tvlm(frm, climate_consumption)
m3 <- fit_simex(frm, climate_consumption, me_vars = c("Precip", "TempMaxAvg"))
m4 <- fit_mixed(frm, climate_consumption, group_var = "Season")
m5 <- fit_hmm(frm, climate_consumption, nstates = 2)
# Compare all models
summary_arvind(m1, m2, m3, m4, m5)
Authors
- Shikhar Tyagi (maintainer) — [email protected]
- Arvind Pandey — [email protected]
License
MIT.