# 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