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The ArvindSt package provides a unified implementation of 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 \((0, \infty)\) with PDF:
\[f(x; \theta) = \frac{\theta(1 + 2x + 2\theta x^2)}{(1 + \theta x)^2} \exp(-\theta x^2), \quad x > 0\]
library(ArvindSt)
# PDF at several points
darvind(c(0.5, 1, 2), theta = 1)
#> [1] 0.86533420 0.45984930 0.02645592
# CDF
parvind(1, theta = 2)
#> [1] 0.9548882
# Quantiles
qarvind(c(0.25, 0.5, 0.75), theta = 1)
#> [1] 0.2515668 0.5223750 0.8715184
# Random generation
set.seed(42)
x <- rarvind(1000, theta = 2)
summary(x)
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> 0.0001702 0.1495542 0.3086652 0.3835834 0.5492802 1.8545692x_seq <- seq(0.01, 4, length.out = 300)
thetas <- c(0.5, 1, 2, 5)
plot(NULL, xlim = c(0, 4), ylim = c(0, 1.5),
xlab = "x", ylab = "f(x)", main = "Arvind PDF Family")
cols <- c("red", "blue", "darkgreen", "purple")
for (i in seq_along(thetas)) {
lines(x_seq, darvind(x_seq, thetas[i]), col = cols[i], lwd = 2)
}
legend("topright", paste("theta =", thetas),
col = cols, lwd = 2, cex = 0.8)
set.seed(42)
x <- rarvind(500, theta = 2)
fit <- fit_arvind_mle(x)
cat("Estimated theta:", fit$theta, "\n")
#> Estimated theta: 2.236184
cat("True theta: 2\n")
#> True theta: 2# Generate simulated data
dat <- simulate_arvind_data(n = 60, seed = 1)
# Fit RW1 model
m1 <- fit_rw1(Y ~ X1 + X2 + X3, dat, seed = 42)
cat("Model:", m1$model_type, "\n")
#> Model: RW1-approx
cat("Theta:", m1$theta, "\n")
#> Theta: 0.1631118
cat("R-squared:", 1 - sum(m1$residuals^2) / sum((m1$Y - mean(m1$Y))^2), "\n")
#> R-squared: 0.935366d1 <- diagnostics_arvind(m1)
d1[, c("Model", "RMSE", "R2", "AIC", "KS_pvalue")]
#> Model RMSE R2 AIC KS_pvalue
#> 1 RW1-approx 4.954889 0.935366 179.2226 0.614732cv1 <- cv_arvind(m1, k_folds = 3, rolling = FALSE, seed = 42)
#> Warning: 'newdata' had 20 rows but variables found have 40 rows
#> Warning: 'newdata' had 20 rows but variables found have 40 rows
#> Warning: 'newdata' had 20 rows but variables found have 40 rows
cat("Mean CV RMSE:", cv1$mean_cv_rmse, "\n")
#> Mean CV RMSE: 27.39963The ArvindSt package provides:
darvind(), parvind(), qarvind(), rarvind()simulate_arvind_data()fit_rw1(), fit_tvlm(), fit_simex(), fit_mixed(), fit_hmm()diagnostics_arvind(), plot_arvind()forecast_arvind()cv_arvind()summary_arvind()These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.