Compositional (version 5.5)

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)
logitnorm.est(x)
hsecant01.est(x, tol = 1e-07)
simplex.est(x, tol = 1e-07)
kumar.est(x, tol = 1e-07)
unitweibull.est(x, tol = 1e-07, maxiters = 100)
ibeta.est(x, tol = 1e-07)
zilogitnorm.est(x)

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.

maxiters

The maximum number of iterations the Newton-Raphson algorithm will perform.

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 some distributions are performed, some of which use the Newton-Raphson. Some distributions and hence the functions do not accept zeros. "logitnorm.mle" fits the logistic normal, hence no Newton-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. The "ibeta.est" fits the zero or the one inflated beta distribution.

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.

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.

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)
# }