View source: R/percentages_mle.R

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

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

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

`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. |

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)

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. |

Michail Tsagris

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

```
diri.nr2,
```

```
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)
```

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