# beta.est: MLE of distributions defined in the (0, 1) interval In Compositional: Compositional Data Analysis

 MLE of distributions defined in the (0, 1) interval 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)
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.

### 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.

### 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.

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.

``` diri.nr2, ```

### 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)
```

Compositional documentation built on July 8, 2022, 1:06 a.m.