# gammamle: MLE of continuous univariate distributions defined on the... In Rfast: A Collection of Efficient and Extremely Fast R Functions

## Description

MLE of continuous univariate distributions defined on the positive line.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```gammamle(x, tol = 1e-09) chisq.mle(x, tol = 1e-09) weibull.mle(x, tol = 1e-09, maxiters = 100) lomax.mle(x, tol = 1e-09) foldnorm.mle(x, tol = 1e-09) betaprime.mle(x, tol = 1e-09) logcauchy.mle(x, tol = 1e-09) loglogistic.mle(x, tol = 1e-09) halfnorm.mle(x) invgauss.mle(x) lognorm.mle(x) pareto.mle(x) expmle(x) exp2.mle(x) maxboltz.mle(x) rayleigh.mle(x) normlog.mle(x) lindley.mle(x) ```

## Arguments

 `x` A vector with positive valued data (zeros are not allowed). `tol` The tolerance level up to which the maximisation stops; set to 1e-09 by default. `maxiters` The maximum number of iterations the Newton-Raphson will perform.

## Details

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. For the t distribution we need the degrees of freedom and estimate the location and scatter parameters. If you want to to fit an inverse gamma distribution simply do "gamma.mle(1/x)". The log-likelihood and the parameters are for the inverse gamma.

The "normlog.mle" is simply the normal distribution where all values are positive. Note, this is not log-normal. It is the normal with a log link. Similarly to the inverse gaussian distribution where the mean is an exponentiated. This comes from the GLM theory.

## 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. `loglik` The value of the maximised log-likelihood. `param` The vector of the parameters.

## Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <mtsagris@uoc.gr> and Manos Papadakis <papadakm95@gmail.com>.

## References

Kalimuthu Krishnamoorthy, Meesook Lee and Wang Xiao (2015). Likelihood ratio tests for comparing several gamma distributions. Environmetrics, 26(8):571-583.

N.L. Johnson, S. Kotz \& N. Balakrishnan (1994). Continuous Univariate Distributions, Volume 1 (2nd Edition).

N.L. Johnson, S. Kotz \& N. Balakrishnan (1970). Distributions in statistics: continuous univariate distributions, Volume 2

Tsagris M., Beneki C. and Hassani H. (2014). On the folded normal distribution. Mathematics, 2(1):12-28.

Sharma V. K., Singh S. K., Singh U. \& Agiwal V. (2015). The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data. Journal of Industrial and Production Engineering, 32(3): 162-173.

You can also check the relevant wikipedia pages for these distributions.

``` zip.mle, normal.mle, beta.mle ```

## Examples

 ```1 2 3 4 5``` ```x <- rgamma(100, 3, 4) system.time( for (i in 1:20) gammamle(x) ) ## system.time( for (i in 1:20) fitdistr(x,"gamma") ) a <- glm(x ~ 1, gaussian(log) ) res<-normlog.mle(x) ```

### Example output

```Loading required package: Rcpp
user  system elapsed
0.018   0.004   0.022
```

Rfast documentation built on Dec. 11, 2021, 9:59 a.m.