MLE of distributions defined in the (0, 1) interval
MLE of distributions defined in the (0, 1) interval.
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) zilogitnorm.est(x)
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" and "simplex.est" use the golden ratio search as is it faster than the Newton-Raphson (less computations). The "zilogitnorm.est" stands for the zero inflated logistic normal distribution.
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. |
Michail Tsagris
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Manos Papadakis <papadakm95@gmail.com>
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.
Zhang, W. & Wei, H. (2008). Maximum likelihood estimation for simplex distribution nonlinear mixed models via the stochastic approximation algorithm. The Rocky Mountain Journal of Mathematics, 38(5): 1863-1875.
You can also check the relevant wikipedia pages.
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)
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