Multivariate Inverse Gaussian Distribution

Provides utilities for estimation for the multivariate inverse Gaussian distribution of Minami (2003) , including random vector generation and explicit estimators of the location vector and scale matrix. The package implements kernel density estimators discussed in Belzile, Desgagnes, Genest and Ouimet (2024) for smoothing multivariate data on half-spaces.

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