MLE of distributions defined in the (0, 1) interval
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@yahoo.gr> and Manos Papadakis <papadakm95@gmail.com>
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)
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