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.
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")
The core of univariateML are the ml*** functions, where *** is a distribution suffix such as norm, gamma, or weibull.
library("univariateML")
mlweibull(egypt$age)
#> Loading required package: intervals
#> Maximum likelihood estimates for the Weibull model
#> shape scale
#> 1.404 33.564
Now we can visually assess the fit of the Weibull model to the egypt data with a plot.
hist(egypt$age, freq = FALSE, xlab = "Mortality", main = "Egypt") lines(mlweibull(egypt$age))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 Gompertz distribution mlgompertz extraDistr Burr distribution mlburr actuar Inverse Burr distribution mlinvburr actuar Birnbaum-Saunders mlfatigue extraDistr Name univariateML function Package Poisson distribution mlpois stats Negative binomial distribution mlnbinom stats Binomial distribution mlbinom stats Geometric distribution mlgeom stats Zipf distribution mlzipf sads Zero-inflated Poisson distribution mlzip extraDistr Discrete uniform distribution mldunif extraDistr Logarithmic series distribution mldunif extraDistr
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(function(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 201.4 244.05 349.978 365.6 422.2 791.9 100
#> naive 8289.4 8652.60 9170.378 8915.3 9288.0 18723.0 100
The maximum likelihood estimators in this package have all been subject to testing, see the tests folder for details.
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 HelpPlease read CONTRIBUTING.md for details about how to contribute or get help.
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