Five Novel Stochastic Regression Models with Arvind-Distributed Errors and Effects

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).

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 Coefficients
  • fit_tvlm() — Time-Varying Coefficient Linear Model
  • fit_simex() — Simulation-Extrapolation
  • fit_mixed() — Mixed-Effects Regression
  • fit_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