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

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

Description

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

Usage

prop.mle(x, distr = "beta", tol = 1e-07, maxiters = 50)

Arguments

x

A numerical vector with proportions, i.e. numbers in (0, 1) (zeros and ones are not allowed).

distr

The distribution to fit. "beta" stands for the beta distribution, "ibeta" for the inflated beta, (0-inflated or 1-inflated, depending on the data), "logitnorm" is the logistic normal and "hsecant01" stands for the hyper-secant.

tol

The tolerance level up to which the maximisation stops.

maxiters

The maximum number of iterations to implement.

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" fits the logistic normal, hence no nwewton-Raphson is required and the "hypersecant01" uses the golden ratio search as is it faster than the Newton-Raphson (less calculations). The distributions included are the Kumaraswamy, zero inflated logistic normal, simplex, unit Weibull and continuous Bernoulli and standard power. Instead of maximising the log-likelihood via a numerical optimiser we have used a Newton-Raphson algorithm which is faster. See wikipedia for the equations to be solved.

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 and Sofia Piperaki.

R implementation and documentation: Michail Tsagris [e-mail] and Sofia Piperaki [e-mail].

References

Kumaraswamy P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology 46(1-2): 79–88.

Jones M.C. (2009). Kumaraswamy's distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6(1): 70–81.

J. Mazucheli, A. F. B. Menezes, L. B. Fernandes, R. P. de Oliveira and M. E. Ghitany (2020). The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. Journal of Applied Statistics, 47(6): 954–974.

Leemis L.M. and McQueston J.T. (2008). Univariate Distribution Relationships. The American Statistician, 62(1): 45–53.

You can also check the relevant wikipedia pages.

See Also

colprop.mle, comp.mle

Examples

x <- rbeta(1000, 1, 4)
prop.mle(x, distr = "beta")