| MLE of distributions defined in the (0, 1) interval {Compositional} | R Documentation |
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)
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. |
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" 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.
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. |
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
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.
You can also check the relevant wikipedia pages.
See Also
Examples
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)