MLE (version 1.5)

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

Description

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

Usage

colreal.mle(x, distr = "normal", v = 5, tol = 1e-07, maxiters = 100, parallel = FALSE)

Value

A matrix with two, columns. The first one contains the parameters of the distribution and the second columns contains the log-likelihood values.

Arguments

x

A numerical vector with data.

distr

The distribution to fit, "normal" stands for the normal distribution, "gumbel" for the Gumbel, "cauchy" for the Cauchy, "logistic" for the logistic distribution, "ct" for the (central) t distribution, "t" for the (non-central) t distribution, "wigner" is the Wigner semicircle distribution and "laplace" is the Laplace distribution. "cauchy0" and "gnormal0" are the Cauchy and generalised normal distributions, respectively, with zero location. The generalised normal distribution is also known as the exponential power distribution or the generalized error distribution.

v

The degrees of freedom of the t distribution.

tol

The tolerance level to stop the iterative process of finding the MLEs.

maxiters

The maximum number of iterations to implement.

parallel

Should the computations take place in parallel?

Author

Michail Tsagris, Sofia Piperaki and Nikolaos Kontemeniotis.

R implementation and documentation: Michail Tsagris , Sofia Piperaki and Nikolaos Kontemeniotis .

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 equation to be solved. For the t distribution we need the degrees of freedom and estimate the location and scatter parameters.

The Cauchy is the t distribution with 1 degree of freedom. The Laplace distribution is also called double exponential distribution.

References

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.

https://en.wikipedia.org/wiki/Wigner_semicircle_distribution

Do M.N. and Vetterli M. (2002). Wavelet-based Texture Retrieval Using Generalised Gaussian Density and Kullback-Leibler Distance. Transaction on Image Processing. 11(2): 146--158.

See Also

real.mle, colpositive.mle, colcirc.mle, coldisc.mle

Examples

x <- rnorm(1000, 10, 2)
a <- real.mle(x, distr = "normal")