Convolving Hyper-Erlang with Hyper-Exponential Distributions Using Linear Algebra

Neumüller C, Robert J, Heuberger A (2022)

Publication Language: English

Publication Type: Conference contribution

Publication year: 2022

Conference Proceedings Title: Proceedings of the 2022 5th International Conference on Mathematics and Statistics

Abstract

In this paper, the sum of a hyper-Erlang and a hyper-exponential distributed random variables is analyzed. Although tedious, the resulting random variable’s probability density function (PDF) can be obtained through convolution of its summands’ PDFs. Alternatively, the resulting distribution can be stated directly in terms of a phase-type distribution. However, computing its PDF can still be very costly and this representation gives little insight on the distribution. It can be shown that the sum of both random variable is again hyper-Erlang distributed of incremented order and can therefore be described without requiring the matrix exponential function. We derive a closed form linear algebra expression for the probability weights of the sum’s hyper-Erlang distribution, which significantly reduces the computational complexity of evaluating its distribution.

Authors with CRIS profile

Clemens Neumüller Lehrstuhl für Informationstechnik mit dem Schwerpunkt Kommunikationselektronik (Stiftungslehrstuhl) Albert Heuberger Lehrstuhl für Informationstechnik mit dem Schwerpunkt Kommunikationselektronik (Stiftungslehrstuhl)

Involved external institutions

Technische Universität Ilmenau

Germany (DE)

How to cite

APA:

Neumüller, C., Robert, J., & Heuberger, A. (2022). Convolving Hyper-Erlang with Hyper-Exponential Distributions Using Linear Algebra. In Proceedings of the 2022 5th International Conference on Mathematics and Statistics.

MLA:

Neumüller, Clemens, Joerg Robert, and Albert Heuberger. "Convolving Hyper-Erlang with Hyper-Exponential Distributions Using Linear Algebra." Proceedings of the ICoMS '22 2022.

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