MLE (version 1.5)

Column-wise MLE of continuous univariate distributions defined on the positive line: Column-wise MLE of continuous univariate distributions defined on the positive line

Description

Column-wise MLE of continuous univariate distributions defined on the positive line.

Usage

colpositive.mle(x, distr = "gamma", tol = 1e-07, maxiters = 100, parallel = FALSE)

Value

A matrix with two, three or five (for the colnormlog.mle) columns. The first one or the first two contain the parameter(s) of the distribution and the other columns contain the log-likelihood values.

Arguments

x

A matrix with positive valued data (zeros are not allowed).

distr

The distribution to fit. "gamma" stands for the gamma distribution, "chisq" for the \(\chi^2\) distribution, "weibull" for the Weibull, "lomax" for the Lomax, "foldnorm" for the folded normal, "betaprime" for the beta-prime distribution, "lognorm" for the log-normal, "logcauchy" for the log-Cauchy, "loglogictic" for the log-logistic distribution. "halfnorm" for the half-normal, "invgauss" for the inverse Gaussian, "pareto" for the Pareto distribution, "exp" for the exponential distribution, "exp2" I do not remember, "maxboltz" for the Maxwell-Boltzman distribution, "rayleigh" is the Rayleigh distribution, "lindley" is the Lindley distribution, "halfcauchy" is the half-Cauchy distribution and "powerlaw" is the power law distribution. The "normlog" 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. The "epois" stands for the exponential-Poisson, the "gep" for the generalized exponential-Poisson and the "pe" for the Poisson-exponential distribution. The "wp" stands for the Weibull Poisson, the "be" for the beta exponential, the "frechet2" for the two-parameter Frechet, for the the "zigamma" and "ziweibull" stand for the zero inflated gamma and Weibull distributions, respectively, and they accept zeros.

tol

The tolerance level up to which the maximisation stops; set to 1e-07 by default.

maxiters

The maximum number of iterations the Newton-Raphson will perform for the Weibull distribution.

parallel

Do you want to calculations to take place in parallel? The default value is FALSE. This is only for the Weibull distribution.

Author

Michail Tsagris, Sofia Piperaki and Rafail Vargiakakis.

R implementation and documentation: Michail Tsagris , Sofia Piperaki and Rafail Vargiakakis .

Details

For each column, the same distribution is fitted and its parameter and log-likelihood are computed.

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

disc.mle, real.mle, prop.mle

Examples

x <- rgamma(100, 3, 4)
positive.mle(x, distr = "gamma")