Flexible modelling in statistics: past, present and future

TL;DR

This paper reviews the evolution and current state of flexible statistical models, highlighting key distribution families and discussing future research directions in handling complex data structures.

Contribution

It provides a comprehensive introduction to flexible modelling, covering historical development, main distribution families, and future challenges for researchers and practitioners.

Findings

Overview of flexible distribution families like skew-normal and g-and-h

Historical narrative of key figures in flexible modelling

Identification of open research questions in flexible modelling

Abstract

In times where more and more data become available and where the data exhibit rather complex structures (significant departure from symmetry, heavy or light tails), flexible modelling has become an essential task for statisticians as well as researchers and practitioners from domains such as economics, finance or environmental sciences. This is reflected by the wealth of existing proposals for flexible distributions; well-known examples are Azzalini's skew-normal, Tukey's $g$-and-$h$, mixture and two-piece distributions, to cite but these. My aim in the present paper is to provide an introduction to this research field, intended to be useful both for novices and professionals of the domain. After a description of the research stream itself, I will narrate the gripping history of flexible modelling, starring emblematic heroes from the past such as Edgeworth and Pearson, then depict three of the most used flexible families of distributions, and finally provide an outlook on future flexible modelling research by posing challenging open questions.