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

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 <[e-mail]> and Manos Papadakis <[e-mail]>.

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 and N. Balakrishnan (1994). Continuous Univariate Distributions, Volume 1 (2nd Edition).

N.L. Johnson, S. Kotz a nd 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. and 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)
for (i in 1:20) gammamle(x)
## for (i in 1:20) fitdistr(x,"gamma")
#a <- glm(x ~ 1, gaussian(log) )
res<-normlog.mle(x)