Multivariate Inverse Gaussian Distribution.

Multivariate inverse Gaussian

This R package consists of utilities for multivariate inverse Gaussian (MIG) models with mean $\boldsymbol{\xi}$ and scale matrix $\boldsymbol{\Omega}$ defined over the halfspace ${\boldsymbol{x} \in \mathbb{R}^d: \boldsymbol{\beta}^\top\boldsymbol{x} > 0}$, including density evaluation and random number generation and kernel smoothing.

Distributions

• mig for the MIG distribution(rmig for random number generation and dmig for density)
• tellipt (rtellipt for random vector generation and dtellipt the density) for truncated Student-$t$ or Gaussian distribution over the half space ${\boldsymbol{x}: \boldsymbol{\beta}^\top\boldsymbol{x}>\delta}$ for $\delta \geq 0$.
• fit_mig to estimate the parameters of the MIG distribution via maximum likelihood (mle) or the method of moments (mom).

Kernel density estimation

• mig_kdens_bandwidth to estimate the bandwidth matrix minimizing the asymptotic mean integrated squared error (AMISE) or the leave-one-out likelihood cross validation, minimizing the Kullback--Leibler divergence. The amise estimators are estimated by drawing from a mig or truncated Gaussian vector via Monte Carlo
• normalrule_bandwidth for the normal rule of Scott for the Gaussian kernel
• mig_kdens for the kernel density estimator
• tellipt_kdens for the truncated Gaussian kernel density estimator.