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

MLE of distributions defined in the (0, 1) interval {Rfast} | 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

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

### See Also

`diri.nr2,`

### Examples

    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)

[Package Rfast version 2.0.0 Index]