An alternative characterization for matrix exponential distributions

Multivariate matrix-exponential distributions

In this extended abstract we define a class of distributions which we shall refer to as multivariate matrix–exponential distributions (MVME). They are defined in a natural way, inspired by the definition of univariate matrix– exponential distributions, as the distributions on R+ having a rational (multidimensional) Laplace transform. A multidimensional rational function is the fraction between ...

Concentrated Matrix Exponential Distributions

We revisit earlier attempts for finding matrix exponential (ME) distributions of a given order with low coefficient of variation (cv). While there is a long standing conjecture that for the first non-trivial order, which is order 3, the cv cannot be less than 0.200902 but the proof of this conjecture is still missing. In previous literature ME distributions with low cv are obtained from special...

Moments Characterization of Order 3 Matrix Exponential Distributions

The class of order 3 phase type distributions (PH(3)) is known to be a proper subset of the class of order 3 matrix exponential distributions (ME(3)). In this paper we investigate the relation of these two sets for what concerns their moment bounds. To this end we developed a procedure to check if a matrix exponential function of order 3 defines a ME(3) distribution or not. This procedure is ba...

Some New Characterization Results on Exponential and Related Distributions

Matrix-exponential distributions: Closure properties

Analysing the properties of a probability distribution is a question of general interest. In this paper we describe the properties of the matrix-exponential class of distributions, developing some properties for the discrete case and proving the closure properties, which for the case of phase-type distributions are extended to the matrix-exponential case, this not being an immediate consequence...