# beta.mle: MLE of distributions defined in the (0, 1) interval In Rfast: A Collection of Efficient and Extremely Fast R Functions

## Description

MLE of distributions defined in the (0, 1) interval.

## Usage

 ```1 2 3 4``` ```beta.mle(x, tol = 1e-09) ibeta.mle(x, tol = 1e-09) logitnorm.mle(x) hsecant01.mle(x, tol = 1e-09) ```

## Arguments

 `x` A numerical vector with proportions, i.e. numbers in (0, 1) (zeros and ones are not allowed). `tol` The tolerance level up to which the maximisation stops.

## Details

Maximum likelihood estimation of the parameters of the beta distribution is performed via Newton-Raphson. The distributions and hence the functions does not accept zeros. "logitnorm.mle" fits the logistic normal, hence no nwewton-Raphson is required and the "hypersecant01.mle" uses the golden ratio search as is it faster than the Newton-Raphson (less calculations)

## Value

A list including:

 `iters` The number of iterations required by the Newton-Raphson. `loglik` The value of the log-likelihood. `param` The estimated parameters. In the case of "hypersecant01.mle" this is called "theta" as there is only one parameter.

## Author(s)

Michail Tsagris

``` diri.nr2, ```
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```x <- rbeta(1000, 1, 4) system.time( for(i in 1:1000) beta.mle(x) ) res<-beta.mle(x) res<-ibeta.mle(x) x <- runif(1000) res<-hsecant01.mle(x) res<-logitnorm.mle(x) res<-ibeta.mle(x) x <- rbeta(1000, 2, 5) x[sample(1:1000, 50)] <- 0 res<-ibeta.mle(x) ```