R: MLE of continuous univariate distributions defined on the...

MLE of continuous univariate distributions defined on the positive line {Rfast} | R Documentation

## MLE of continuous univariate distributions defined on the positive line

### Description

MLE of continuous univariate distributions defined on the positive line.

### Usage

    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.

### See Also

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

### Examples

    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)

[Package Rfast version 2.0.4 Index]