MLE of some continuous multivariate distributions {MLE}

MLE of some continuous multivariate distributions

Description

MLE of some continuous multivariate distributions.

Usage

mv.mle(x, distr = "mvnorm", v = 1, tol = 1e-7)

Arguments

x

A matrix with numerical data.

distr

The distribution to fit. "mvnorm" stands for the multivariate normal distribution, "mvlnorm" for the multivariate log-normal, "mvt" is the multivariate t distribution and "invdir" stands for the inverse Dirichlet distribution. If you want the multivariate Cauchy distribution, simply choose "mvt" and set the v argument equal to 1.

v

The degrees of freedom. Must be a positive number, greater than zero.

tol

The tolerance value to terminate the EM algorithm.

Details

The mean vector, covariance matrix and the value of the log-likelihood of the multivariate normal or log-normal distribution is calculated. For the log-normal distribution we also provide the expected value and the covariance matrix. The location vector, scatter matrix and the value of the log-likelihood for the multivariate t distribution is calculated. Maximum likelihood estimation of the parameters of the inverted is performed via Newton-Raphson.

Value

A list including:

loglik

The log-likelihood multivariate distribution.

mu

The mean vector.

sigma

The covariance matrix.

m

The expected mean vector of the multivariate log-normal distribution.

s

The expected covariance matrix of the multivariate log-normal distribution.

Author(s)

Michail Tsagris and Sofia Piperaki.

R implementation and documentation: Michail Tsagris [e-mail] and Sofia Piperaki [e-mail].

References

Kotz S., Balakrishnan N. and Johnson N. L. (2004). Continuous multivariate distributions, Volume 1: Models and applications (Vol. 1). John wiley & sons.

Nadarajah S. and Kotz S. (2008). Estimation methods for the multivariate t distribution. Acta Applicandae Mathematicae, 102(1): 99–118.

Bdiri T. and Bouguila N. (2012). Positive vectors clustering using inverted Dirichlet finite mixture models. Expert Systems with Applications, 39(2): 1869–1882.

http://isi.cbs.nl/iamamember/CD2/pdf/329.PDF

https://en.wikipedia.org/wiki/Log-normal_distribution#Multivariate_log-normal

See Also

real.mle

Examples

x <- matrix( rnorm(100 * 5), ncol = 5)
res <- mv.mle(x)