ECden_vec {TOHM}

Compute the Euler characteristic densities

Description

Compute the Euler characteristic (EC) densities for Gaussian, Chi-square and Chi-bar-square random fields up to a given order.

Usage

ECden_vec(c, D, type = c("Gaussian", "Chi^2", "Chi-bar^2"),  
k = NULL, k_vec = NULL, weights = NULL)

Arguments

c

Value on which the EC densities are evaluated.

D

Maximum order of the EC density to be computed.

type

Type of random field. The possible options are "Gaussian", "Chi^2", and "Chi-bar^2". See details.

k

If type="Chi^2", degrees of freedom of the Chi-square random field.

k_vec

If type="Chi-bar^2" the degrees of freedom of the Chi-square random fields in the mixture.

weights

If type="Chi-bar^2" the weights of the mixure of Chi-square random fields in the mixture. The ordering should be the same as in k_vec.

Details

If type="Chi-bar^2" the degrees of freedom of the Chi-square random fields involved in the mixture, as well as the respective weights, have to be spefcified in the arguments k_vec and weights.

Value

Returns the values of the EC densities of order zero up to the dimension of the search area considered and evaluated at c.

Author(s)

Sara Algeri

References

R.J. Adler and J.E. Taylor. Random fields and geometry. Springer Science and Business Media, 2009.

J.E. Taylor and K.J.Worsley. Detecting sparse cone alternatives for gaussian random fields, with an application to fmri. Statistica Sinica, 2013.

See Also

chi2_ECden, Gauss_ECden

Examples

ECden_vec(12,2,"Chi-bar^2",k_vec=c(0,1),weights=c(0.5,0.5))