univariateML

Overview

univariateML is an R-package for user-friendly maximum likelihood estimation of a selection of parametric univariate densities and probability mass functions. In addition to basic estimation capabilities, this package support visualization through plot and qqmlplot, model selection by AIC and BIC, confidence sets through the parametric bootstrap with bootstrapml, and convenience functions such as the density, distribution function, quantile function, and random sampling at the estimated distribution parameters.

Installation

Use the following command from inside R to install from CRAN.

install.packages("univariateML")

Or install the development version from Github.

# install.packages("devtools")
devtools::install_github("JonasMoss/univariateML")

Usage

The core of univariateML are the ml*** functions, where *** is a distribution suffix such as norm, gamma, or weibull.

library("univariateML")
mlweibull(egypt$age)
#> Maximum likelihood estimates for the Weibull model 
#>  shape   scale  
#>  1.404  33.564

Now we can visually assess the fit of the Weibull model to the egypt data with a plot.

hist(egypt$age, freq = FALSE, xlab = "Mortality", main = "Egypt")
lines(mlweibull(egypt$age))

Supported densities

Name	univariateML function	Package
Cauchy distribution	mlcauchy	stats
Gumbel distribution	mlgumbel	extraDistr
Laplace distribution	mllaplace	extraDistr
Logistic distribution	mllogis	stats
Normal distribution	mlnorm	stats
Student t distribution	mlstd	fGarch
Generalized Error distribution	mlged	fGarch
Skew Normal distribution	mlsnorm	fGarch
Skew Student t distribution	mlsstd	fGarch
Skew Generalized Error distribution	mlsged	fGarch
Beta prime distribution	mlbetapr	extraDistr
Exponential distribution	mlexp	stats
Gamma distribution	mlgamma	stats
Inverse gamma distribution	mlinvgamma	extraDistr
Inverse Gaussian distribution	mlinvgauss	actuar
Inverse Weibull distribution	mlinvweibull	actuar
Log-logistic distribution	mlllogis	actuar
Log-normal distribution	mllnorm	stats
Lomax distribution	mllomax	extraDistr
Rayleigh distribution	mlrayleigh	extraDistr
Weibull distribution	mlweibull	stats
Log-gamma distribution	mllgamma	actuar
Pareto distribution	mlpareto	extraDistr
Beta distribution	mlbeta	stats
Kumaraswamy distribution	mlkumar	extraDistr
Logit-normal	mllogitnorm	logitnorm
Uniform distribution	mlunif	stats
Power distribution	mlpower	extraDistr
Poisson distribution	mlpois	stats

Implementations

Analytic formulae for the maximum likelihood estimates are used whenever they exist. Most ml*** functions without analytic solutions have a custom made Newton-Raphson solver. These can be much faster than a naïve solution using nlm or optim. For example, mlbeta has a large speedup over the naïve solution using nlm.

# install.packages("microbenchmark")
set.seed(313)
x <- rbeta(500, 2, 7)

microbenchmark::microbenchmark(
  univariateML = univariateML::mlbeta(x),
  naive = nlm(\(p) -sum(dbeta(x, p[1], p[2], log = TRUE)), p = c(1, 1))
)
#> Unit: microseconds
#>          expr     min       lq      mean   median       uq      max neval
#>  univariateML   205.1   329.85   800.077   464.35   730.35  13938.4   100
#>         naive 10665.9 11773.30 21428.104 15233.70 28628.65 103372.1   100

The maximum likelihood estimators in this package have all been subject to testing, see the tests folder for details.

Documentation

For an overview of the package and its features see the overview vignette. For an illustration of how this package can make an otherwise long and laborious process much simpler, see the copula vignette.

How to Contribute or Get Help

Please read CONTRIBUTING.md for details about how to contribute or get help.