MLE of distributions defined in the (0, 1) interval.
prop.mle(x, distr = "beta", tol = 1e-07, maxiters = 50)A list including:
The number of iterations required by the Newton-Raphson.
The value of the log-likelihood.
The estimated parameters. In the case of "hypersecant01.mle" this is called "theta" as there is only one parameter.
A numerical vector with proportions, i.e. numbers in (0, 1) (zeros and ones are not allowed).
The distribution to fit. "beta" stands for the beta distribution, "logitnorm" is the logistic normal, "unitweibull" is the unit-Weibull and the "sp" is the standard power distribution, "ibeta" is the inflated beta, (0-inflated or 1-inflated, depending on the data), "hsecant01" stands for the hyper-secant, "kumar" is the Kumaraswamy, "simplex" is the simplex distribution, "zil" is the zero inflated logistic normal, and "cbern" is the continuous Bernoulli distribution.
The tolerance level up to which the maximisation stops.
The maximum number of iterations to implement.
Michail Tsagris and Sofia Piperaki.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Sofia Piperaki sofiapip23@gmail.com.
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.
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.
colprop.mle, comp.mle
x <- rbeta(1000, 1, 4)
prop.mle(x, distr = "beta")
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