R: MLE of continuous univariate distributions defined on the...

MLE of continuous univariate distributions defined on the real line {Rfast} | R Documentation

## MLE of continuous univariate distributions defined on the real line

### Description

MLE of continuous univariate distributions defined on the real line.

### Usage

    normal.mle(x)
    gumbel.mle(x, tol = 1e-09)
    cauchy.mle(x, tol = 1e-09)
    logistic.mle(x, tol = 1e-07)
    ct.mle(x, tol = 1e-09)
    tmle(x, v = 5, tol = 1e-08)
    wigner.mle(x, tol = 1e-09)
    laplace.mle(x)

### Arguments

`x` | A numerical vector with data.
`v` | The degrees of freedom of the t distribution.
`tol` | The tolerance level up to which the maximisation stops set to 1e-09 by default.

### Details

Instead of maximising the log-likelihood via a numerical optimiser we have used a Newton-Raphson algorithm which is faster. See wikipedia for the equation to be solved. For the t distribution we need the degrees of freedom and estimate the location and scatter parameters.

The Cauchy is the t distribution with 1 degree of freedom. If you want to fit such a distribution used the cauchy.mle and not the t.mle with 1 degree of freedom as it's faster. The Laplace distribution is also called double exponential distribution.

The wigner.mle refers to the wigner semicircle distribution.

### Value

Usually a list with three elements, but this is not for all cases.

`iters` | The number of iterations required for the Newton-Raphson to converge.
`loglik` | The value of the maximised log-likelihood.
`param` | The vector of the parameters.

### Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <mtsagris@uoc.gr> and Manos Papadakis <papadakm95@gmail.com>.

### References

Johnson, Norman L. Kemp, Adrianne W. Kotz, Samuel (2005). Univariate Discrete Distributions (third edition). Hoboken, NJ: Wiley-Interscience.

https://en.wikipedia.org/wiki/Wigner_semicircle_distribution

### See Also

`zip.mle, gammamle, vm.mle`

### Examples

    x <- rt(1000,10)
    a <- ct.mle(x)
    res<-tmle(x, v = a$nu)
    res<-cauchy.mle(x)
    res<-normal.mle(x)
    res<-logistic.mle(x)
    res<-gumbel.mle(x)

[Package Rfast version 2.0.4 Index]