"TBEinf" computes the density of $\text{TBE}\infty$ by direct calculation, saddlepoint approximation, Fourier inversion, and related methods. "TBEinf" applys $\text{TBE}\infty$ to the generalized linear model for estimation and prediction. The estimation of coefficients is obtained through Iteratively Reweighted Least Squares.
#install Rtools 3.5 (http://cran.r-project.org/bin/windows/Rtools)
#install.packages("devtools")
#install.packages("Rcpp")
library(devtools)
install_github("xliusufe/TBEinf")
- TBEinf-manual ------------ Details of the usage of the package.
library(TBEinf)
library(pracma)
set.seed(123)
n <- 800
p <- 15
pp <- p+1
beta_0 <- -0.5*(1:pp)
phi_0 <- 0.05
x <- matrix(runif(n * p), nrow = n, ncol = p)
X <- cbind(1, x)
eta_0 <- X %*% beta_0
m_0 <- -log(- eta_0)
y <- rnorm(n, mean = m_0, sd = phi_0*exp(m_0))
initial <- rep(-0.1, pp)
beta <- TBEinf.glm.fit(y, X, initial)$beta
phi <- TBEinf.glm.fit(y, X, initial)$phi
x_new <- runif(pp)
y_pre <- TBEinf.glm.pre(x_new, beta)
Bar-Lev, S.K. (2023). The Exponential Dispersion Model Generated by the Landau Distribution ---A Comprehensive Review and Further Developments. Mathematics. 11(20), 4343.
Dunn, P. K. and Smyth, G. K. (2008). Evaluation of Tweedie exponential dispersion model densities by Fourier inversion. Statistics and Computing. 18, 73--86.
Dunn, P. K. and Smyth, G. K. (2018). Generalized Linear Models with Examples in R. Springer: Berlin/Heidelberg, Germany.
Dunn, P. K. and Smyth, G. K. (2022). Evaluation of Tweedie Exponential Family Models; R Package Version 2.3.5; 2022. Available online: https://cran.r-project.org/web/packages/tweedie/tweedie.pdf
Jorgensen, B. (1997). The Theory of Dispersion Models. Chapman and Hall, London.
Sidi, Avram (1988). A user-friendly extrapolation method for oscillatory infinite integrals. Mathematics of Computation. 51(183), 249--266.
The R-package is developed by Ziyu Xiang (xiangziyu2867@163.com), Xu Liu, Shaul Bar-Lev, Ad Ridder.