Column-wise MLE of distributions defined in the (0, 1) interval.
colprop.mle(x, distr = "beta", tol = 1e-07, maxiters = 100, parallel = FALSE)A matrix with two, columns. The first one contains the parameters of the distribution and the second columns contains the log-likelihood values.
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 the Newton-Raphson will perform.
Should the computations take place in parallel? This is for the "spml" only.
Michail Tsagris, Sofia Piperaki and Rafail Vargiakakis.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr, Sofia Piperaki sofiapip23@gmail.com and Rafail Vargiakakis rafailvargiakakis@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.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).
N.L. Johnson, S. Kotz and N. Balakrishnan (1994). Continuous Univariate Distributions, Volume 1 (2nd Edition).
N.L. Johnson, S. Kotz and N. Balakrishnan (1970). Distributions in statistics: continuous univariate distributions, Volume 2.
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.
prop.mle, positive.mle
x <- rbeta(1000, 1, 4)
prop.mle(x, distr = "beta")
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