`univariateML`

is an `R`

-package for user-friendly maximum likelihood
estimation of a selection
of parametric univariate densities. 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")
::install_github("JonasMoss/univariateML") devtools
```

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))
```

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 |

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)
<- rbeta(500, 2, 7)
x
::microbenchmark(
microbenchmarkunivariateML = 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 259.2 348.75 557.959 447.05 536.40 5103.5 100
#> naive 15349.1 15978.35 16955.165 16365.45 17082.25 48941.4 100
```

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.

Please read `CONTRIBUTING.md`

for details about how to
contribute or get help.