These are the currently implemented distributions.
Name | univariateML function | Package | Parameters | Support |
---|---|---|---|---|
Cauchy distribution | mlcauchy |
stats | location ,scale |
\(\mathbb{R}\) |
Gumbel distribution | mlgumbel |
extraDistr | mu , sigma |
\(\mathbb{R}\) |
Laplace distribution | mllaplace |
extraDistr | mu , sigma |
\(\mathbb{R}\) |
Logistic distribution | mllogis |
stats | location ,scale |
\(\mathbb{R}\) |
Normal distribution | mlnorm |
stats | mean , sd |
\(\mathbb{R}\) |
Student t distribution | mlstd |
fGarch | mean , sd , nu |
\(\mathbb{R}\) |
Generalized Error distribution | mlged |
fGarch | mean , sd , nu |
\(\mathbb{R}\) |
Skew Normal distribution | mlsnorm |
fGarch | mean , sd , xi |
\(\mathbb{R}\) |
Skew Student t distribution | mlsstd |
fGarch | mean , sd , nu , xi |
\(\mathbb{R}\) |
Skew Generalized Error distribution | mlsged |
fGarch | mean , sd , nu , xi |
\(\mathbb{R}\) |
Beta prime distribution | mlbetapr |
extraDistr | shape1 , shape2 |
\((0, \infty)\) |
Exponential distribution | mlexp |
stats | rate |
\([0, \infty)\) |
Gamma distribution | mlgamma |
stats | shape ,rate |
\((0, \infty)\) |
Inverse gamma distribution | mlinvgamma |
extraDistr | alpha , beta |
\((0, \infty)\) |
Inverse Gaussian distribution | mlinvgauss |
actuar | mean , shape |
\((0, \infty)\) |
Inverse Weibull distribution | mlinvweibull |
actuar | shape , rate |
\((0, \infty)\) |
Log-logistic distribution | mlllogis |
actuar | shape , rate |
\((0, \infty)\) |
Log-normal distribution | mllnorm |
stats | meanlog , sdlog |
\((0, \infty)\) |
Lomax distribution | mllomax |
extraDistr | lambda , kappa |
\([0, \infty)\) |
Rayleigh distribution | mlrayleigh |
extraDistr | sigma |
\([0, \infty)\) |
Weibull distribution | mlweibull |
stats | shape ,scale |
\((0, \infty)\) |
Log-gamma distribution | mllgamma |
actuar | shapelog , ratelog |
\((1, \infty)\) |
Pareto distribution | mlpareto |
extraDistr | a , b |
\([b, \infty)\) |
Beta distribution | mlbeta |
stats | shape1 ,shape2 |
\((0, 1)\) |
Kumaraswamy distribution | mlkumar |
extraDistr | a , b |
\((0, 1)\) |
Logit-normal | mllogitnorm |
logitnorm | mu , sigma |
\((0, 1)\) |
Uniform distribution | mlunif |
stats | min , max |
\([\min, \max]\) |
Power distribution | mlpower |
extraDistr | alpha , beta |
\([0, a)\) |
This package follows a naming convention for the ml***
functions. To access the
documentation of the distribution associated with an ml***
function, write package::d***
.
For instance, to find the documentation for the log-gamma distribution write
?actuar::dlgamma
The maximum likelihood estimator of the Lomax distribution frequently fails to exist. For assume \(\kappa\to\lambda^{-1}\overline{x}^{-1}\) and \(\lambda\to0\). The density \(\lambda\kappa\left(1+\lambda x\right)^{-\left(\kappa+1\right)}\) is approximately equal to \(\lambda\kappa\left(1+\lambda x\right)^{-\left(\lambda^{-1}\overline{x}^{-1}+1\right)}\) when \(\lambda\) is small enough. Since \(\lambda\kappa\left(1+\lambda x\right)^{-\left(\lambda^{-1}\overline{x}^{-1}+1\right)}\to\overline{x}^{-1}e^{-\overline{x}^{-1}x}\), the density converges to an exponential density.
eps = 0.1
x = seq(0, 3, length.out = 100)
plot(dexp, 0, 3, xlab = "x", ylab = "Density", main = "Exponential and Lomax")
lines(x, extraDistr::dlomax(x, lambda = eps, kappa = 1/eps), col = "red")