Compound Power Series Distribution with Negative Multinomial Summands

Characterisation and Risk Process

Authors

  • Pavlina Jordanova Shumen University
  • Monika Petkova Sofia University
  • Milan Stehlík Johannes Kepler University

DOI:

https://doi.org/10.57805/revstat.v18i1.287

Keywords:

power series distributions, Multivariate Compound distribution, Negative multinomial distribution, risk process

Abstract

The paper considers a multivariate distribution whose coordinates are compounds. The number of the summands is itself also a multivariate compound with one and the same univariate Power series distributed number of summands and negative multinomially distributed summands. In the total claims amount process the summands are independent identically distributed random vectors. We provide the first full characterization of this distribution. We show that considered as a mixture this distribution would be Mixed Negative multinomial distribution having the possibly scale changed power series distributed THE first parameter. We provide an interesting application to risk theory.

Published

2022-01-12

How to Cite

Jordanova, P., Petkova , M., & Stehlík , M. (2022). Compound Power Series Distribution with Negative Multinomial Summands: Characterisation and Risk Process. REVSTAT-Statistical Journal, 18(1), 47–69. https://doi.org/10.57805/revstat.v18i1.287