MLE of distributions defined for proportions {Rfast2}

MLE of distributions defined for proportions

Description

MLE of distributions defined for proportions.

Usage

kumar.mle(x, tol = 1e-07, maxiters = 50)
simplex.mle(x, tol = 1e-07)
zil.mle(x)
unitweibull.mle(x, tol = 1e-07, maxiters = 100) 
cbern.mle(x, tol = 1e-6) 
sp.mle(x)

Arguments

x

A vector with proportions or percentages. Zeros are allowed only for the zero inflated logistirc normal distribution (zil.mle).

tol

The tolerance level up to which the maximisation stops.

maxiters

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

Details

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

Usually a list with three elements, but this is not for all cases.

iters

The number of iterations required for the Newton-Raphson to converge.

param

The two parameters (shape and scale) of the Kumaraswamy distribution. For the zero inflated logistic normal, the probability of non zeros, the mean and the unbiased variance.

loglik

The value of the maximised log-likelihood.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [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.

Mazucheli J., Menezes A.F.B., Fernandes L.B., de Oliveira R.P. and Ghitany M.E. (2020). The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. Journal of Applied Statistics, DOI:10.1080/02664763.2019.1657813

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

zigamma.mle, censweibull.mle

Examples

u <- runif(1000)
a <- 0.4  ;  b <- 1
x <- ( 1 - (1 - u)^(1/b) )^(1/a)
kumar.mle(x)