knitr::opts_chunk$set(echo = TRUE)
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")
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