# normal.mle: MLE of continuous univariate distributions defined on the... In Rfast: A Collection of Efficient and Extremely Fast R Functions

## Description

MLE of continuous univariate distributions defined on the real line.

## Usage

 ```1 2 3 4 5 6 7 8``` ```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.

Michail Tsagris

## 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

``` zip.mle, gammamle, vm.mle ```
 ```1 2 3 4 5 6 7``` ```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) ```