Compositional (version 4.1)

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

Description

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

Usage

beta.est(x, tol = 1e-07)
ibeta.est(x, tol = 1e-07)
logitnorm.est(x)
hsecant01.est(x, tol = 1e-07)
simplex.est(x, tol = 1e-07)
kumar.est(x, tol = 1e-07)

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.

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.est" this is called "theta" as there is only one parameter.

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" and "simplex.est" use the golden ratio search as is it faster than the Newton-Raphson (less computations).

See Also

diri.nr2,

Examples

# NOT RUN {
x <- rbeta(1000, 1, 4)
beta.est(x)
ibeta.est(x)

x <- runif(1000)
hsecant01.est(x)
logitnorm.est(x)
ibeta.est(x)

x <- rbeta(1000, 2, 5)
x[sample(1:1000, 50)] <- 0
ibeta.est(x)
# }