estparmggd {mggd}

Estimation of the Parameters of a Multivariate Generalized Gaussian Distribution

Description

Estimation of the mean vector, dispersion matrix and shape parameter of a multivariate generalized Gaussian distribution (MGGD).

Usage

estparmggd(x, eps = 1e-6, display = FALSE, plot = display)

Arguments

x

numeric matrix or data frame.

eps

numeric. Precision for the estimation of the beta parameter.

display

logical. When TRUE the value of the beta parameter at each iteration is printed.

plot

logical. When TRUE the successive values of the beta parameter are plotted, allowing to visualise its convergence.

Details

The \mu parameter is the mean vector of x.

The dispersion matrix \Sigma and shape parameter: \beta are computed using the method presented in Pascal et al., using an iterative algorithm.

The precision for the estimation of beta is given by the eps parameter.

Value

A list of 3 elements:

• mu the mean vector.

• Sigma: symmetric positive-definite matrix. The dispersion matrix.

• beta non-negative numeric value. The shape parameter.

with two attributes attr(, "epsilon") (precision of the result) and attr(, "k") (number of iterations).

Author(s)

Pierre Santagostini, Nizar Bouhlel

References

F. Pascal, L. Bombrun, J.Y. Tourneret, Y. Berthoumieu. Parameter Estimation For Multivariate Generalized Gaussian Distribution. IEEE Trans. Signal Processing, vol. 61 no. 23, p. 5960-5971, Dec. 2013. doi: 10.1109/TSP.2013.2282909

See Also

dmggd: probability density of a MGGD.

rmggd: random generation from a MGGD.

Examples

mu <- c(0, 1, 4)
Sigma <- matrix(c(0.8, 0.3, 0.2, 0.3, 0.2, 0.1, 0.2, 0.1, 0.2), nrow = 3)
beta <- 0.74
x <- rmggd(100, mu, Sigma, beta)

# Estimation of the parameters
estparmggd(x)