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

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

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

### Description

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

### Usage

``````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, ```

### Examples

``````x <- rbeta(1000, 1, 4)
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)

``````

Rfast documentation built on Nov. 9, 2023, 5:06 p.m.