estparmggd function

Estimation of the Parameters of a Multivariate Generalized Gaussian Distribution

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

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.

Returns

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).

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.

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)

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. tools:::Rd_expr_doi("DOI:10.1109/TSP.2013.2282909")

See Also

dmggd: probability density of a MGGD.

rmggd: random generation from a MGGD.

Author(s)

Pierre Santagostini, Nizar Bouhlel