mvdist

r_mvnorm

r_mvt

r_mvlnorm

r_mvskewnorm

r_dirichlet

r_mvmixture

Random generation for common multivariate distributions. All functions
return an <code>n x d</code> matrix with column names, and accept an optional <code>seed</code>.<ul>
<li><code>r_mvnorm()</code>: multivariate normal \(N(\mu, \Sigma)\).</li>
<li><code>r_mvt()</code>: multivariate Student-t with <code>df</code> degrees of freedom and
scale matrix <code>sigma</code>.</li>
<li><code>r_mvlnorm()</code>: multivariate log-normal: <code><a href="/link/exp()?package=SynthesizerPlus&version=0.4.0" data-mini-rdoc="SynthesizerPlus::exp()">exp()</a></code> of a multivariate normal
with parameters <code>meanlog</code>, <code>sigmalog</code>.</li>
<li><code>r_mvskewnorm()</code>: multivariate skew-normal of Azzalini and Dalla Valle
(1996) with location <code>xi</code>, scale matrix <code>omega</code> and shape <code>alpha</code>.</li>
<li><code>r_dirichlet()</code>: Dirichlet distribution on the simplex, generated by
normalising gamma draws. Draws are computed on the log scale (with the
\(Y U^{1/a}\) boost for shapes below 1), so very small concentration
parameters do not underflow to <code>0/0</code>; as \(\alpha \to 0\) the draws
approach the vertices of the simplex.</li>
<li><code>r_mvmixture()</code>: finite mixture of multivariate normals.</li>
</ul>

Generates synthetic versions of numeric, categorical, mixed-type
and time-series data. Marginal distributions are modelled with
interpolated empirical quantile functions and dependence with Gaussian or
Student-t copulas (Sklar, 1959). Discrete and categorical variables enter
the copula through the distributional transform (Ruschendorf, 2009,
<doi:10.1016/j.jspi.2009.05.030>), and their latent correlations are
estimated by maximum likelihood as polychoric (Olsson, 1979,
<doi:10.1007/BF02296207>) and polyserial (Olsson, Drasgow and Dorans,
1982, <doi:10.1007/BF02294164>) correlations. Unordered categories are
placed on their latent coordinate in an order estimated from their
association with the other variables. Missing values are
modelled by missingness indicators inside the copula, so that
missingness may depend on other variables. Supports stratified models,
a closeness parameter with calibration to a target distance or
disclosure-risk level, chunked generation of very large data sets,
optional hybrid copula and conditional CART or GAM synthesis for
one continuous response (requiring 'rpart' or 'mgcv'), training-only
automatic selection of the conditional engine, experimental nominal
conditional synthesis of one unordered categorical response (requiring
'nnet'), copula vector-autoregressive and bootstrap time-series synthesis,
augmentation of small training sets for machine learning, and random
generation from multivariate distributions and elliptical and
Archimedean copulas. Fidelity, utility and disclosure risk are assessed
with marginal distances, association matrices, propensity score
mean-squared error (Snoke et al., 2018, <doi:10.1111/rssa.12358>),
confidence-interval overlap, correct attribution probability and
distance to closest record, with 'ggplot2' visualisations. Data can be
read from and written to CSV, TSV, RDS, RData, Parquet, Feather, HDF5,
JSON, NDJSON, Excel, SPSS, Stata, SAS and fst files. The
empirical-quantile and copula approach builds on ideas of the
'synthesizer' package by Mark van der Loo.

Bogdan Oancea

SynthesizerPlus

Synthetic Data Generation with Copulas, Evaluation and
Multi-Format I/O

mvdist function

<dl><dt>n</dt>
<dd>Number of draws.</dd>
<dt>mean, xi</dt>
<dd>Mean / location vector (finite; defaults to zero).</dd>
<dt>sigma, omega</dt>
<dd>Covariance (scale) matrix: square, finite, symmetric
and positive semi-definite. <code>omega</code> must also have a strictly positive
diagonal, because the skew-normal is parameterised through the
correlation matrix \(\bar\Omega = \omega^{-1}\Omega\omega^{-1}\).
<code>sigma</code> may be singular (positive semi-definite), giving a degenerate
normal or t distribution; <code>omega</code> must be positive definite, as in
the standard definition of the skew-normal density.</dd>
<dt>seed</dt>
<dd>Optional random seed.</dd>
<dt>df</dt>
<dd>Degrees of freedom (<code>Inf</code> gives the normal distribution).</dd>
<dt>meanlog, sigmalog</dt>
<dd>Mean vector and covariance matrix on the log scale.</dd>
<dt>alpha</dt>
<dd>Shape (skewness) vector for <code>r_mvskewnorm()</code>; concentration
vector for <code>r_dirichlet()</code>.</dd>
<dt>weights</dt>
<dd>Mixture weights (normalised internally).</dd>
<dt>means</dt>
<dd>List of component mean vectors.</dd>
<dt>sigmas</dt>
<dd>List of component covariance matrices.</dd>
<dt>return_component</dt>
<dd>Should <code>r_mvmixture()</code> add the component label as
attribute <code>"component"</code>?</dd></dl>

Arguments

Random generation for common multivariate distributions. All functions
return an <code>n x d</code> matrix with column names, and accept an optional <code>seed</code>.<ul>
<li><code>r_mvnorm()</code>: multivariate normal \(N(\mu, \Sigma)\).</li>
<li><code>r_mvt()</code>: multivariate Student-t with <code>df</code> degrees of freedom and
scale matrix <code>sigma</code>.</li>
<li><code>r_mvlnorm()</code>: multivariate log-normal: <code><a href='https://rdrr.io/r/base/Log.html'>exp()</a></code> of a multivariate normal
with parameters <code>meanlog</code>, <code>sigmalog</code>.</li>
<li><code>r_mvskewnorm()</code>: multivariate skew-normal of Azzalini and Dalla Valle
(1996) with location <code>xi</code>, scale matrix <code>omega</code> and shape <code>alpha</code>.</li>
<li><code>r_dirichlet()</code>: Dirichlet distribution on the simplex, generated by
normalising gamma draws. Draws are computed on the log scale (with the
\(Y U^{1/a}\) boost for shapes below 1), so very small concentration
parameters do not underflow to <code>0/0</code>; as \(\alpha \to 0\) the draws
approach the vertices of the simplex.</li>
<li><code>r_mvmixture()</code>: finite mixture of multivariate normals.</li>
</ul>

Multivariate random number generators — mvdist

<dl>

<dt>n</dt>
<dd>Number of draws.</dd>


<dt>mean, xi</dt>
<dd>Mean / location vector (finite; defaults to zero).</dd>


<dt>sigma, omega</dt>
<dd>Covariance (scale) matrix: square, finite, symmetric
and positive semi-definite. <code>omega</code> must also have a strictly positive
diagonal, because the skew-normal is parameterised through the
correlation matrix \(\bar\Omega = \omega^{-1}\Omega\omega^{-1}\).
<code>sigma</code> may be singular (positive semi-definite), giving a degenerate
normal or t distribution; <code>omega</code> must be positive definite, as in
the standard definition of the skew-normal density.</dd>


<dt>seed</dt>
<dd>Optional random seed.</dd>


<dt>df</dt>
<dd>Degrees of freedom (<code>Inf</code> gives the normal distribution).</dd>


<dt>meanlog, sigmalog</dt>
<dd>Mean vector and covariance matrix on the log scale.</dd>


<dt>alpha</dt>
<dd>Shape (skewness) vector for <code>r_mvskewnorm()</code>; concentration
vector for <code>r_dirichlet()</code>.</dd>


<dt>weights</dt>
<dd>Mixture weights (normalised internally).</dd>


<dt>means</dt>
<dd>List of component mean vectors.</dd>


<dt>sigmas</dt>
<dd>List of component covariance matrices.</dd>


<dt>return_component</dt>
<dd>Should <code>r_mvmixture()</code> add the component label as
attribute <code>"component"</code>?</dd>

</dl>

mvdist: Multivariate random number generators

Description

Usage

Value

Arguments

References

Examples