chapter  Chapter 8
30 Pages

On Parameter Dependence and Related Topics: The Impact of Jerzy Filus from Genesis to Recent Developments

WithJerzy Filus, Lidia Filus, Barry C. Arnold, Pavlina K. Jordanova, Ludy Núñez Soza, Ying Lu, Silvia Stehlíková, Milan Stehlík

This chapter discusses via an interview with Jerzy Filus about his career from his early years in Poland all the way up to today, we will unfold and explore the genesis and development of multivariate pseudonormal distributions, parameter dependence, and finally stochastic dependence in general. As a kind of fusion of the two approaches, the common paper Filus, Filus, and Arnold demonstrated a method of extension of the bivariate normal density where only six parameters were needed; in the Arnold et al. approach, eight parameters were needed as a minimum. In Filus and Filus, the authors gave a reliability motivation for pseudonormal distributions using the parameter dependence paradigm. In this area, Jerzy Filus and coauthors have made substantial recent developments on this topic and propose an interesting new model. In Filus, Filus and Stehlík, a statistical study was conducted related to bivariate pseudoexponential distribution via its survival function, which allows to model other multiple failures.