Distribution Parameters Structure

Since by design, we keep the distribution parameters apart from the distribution structure, many functions of the distributions require a parameter structure theta to be passed in, or output this parameter structure. In what follows we describe this structure in detail (well, there is not that much detail, actually).

Structure Description

theta is a structure with field names corresponding to parameter names defined in the respective distribution, and values equal to the desired parameter values.

Example

The parameters for a multi-variate normal distribution are mu for the mean, and sigma for the covariance matrix. So we can construct a parameter structure for this distribution like this:

theta = struct('mu', [1; 2], 'sigma', [2 1; 3 4]);

or equivalently like this:

theta.mu = [1; 2];
theta.sigma = [2 1; 3 4];

Then we can pass theta to the distribution functions. For example:

D = mvnfactory(2);
h = D.entropy(theta)
h =
    3.8108

Relation with Manopt Manifolds

MixEst distribution parameter structures (theta) are actually points on some specific manifold representing the compound geometry of valid values for all of the parameters of the distribution. The manifold is created using the productmanifold function from the Manopt toolbox to build a product of the manifolds corresponding to each parameter, and therefore you can work with the value of each parameter using a field in theta.

The Manopt manifold of parameters for a distribution structure D can be accessed using D.M.