Exploring the equivalence of two common mixture models for duration data

Fader, P S, Hardie, B G S, McCarthy, D and Vaidyananathan, R (2019) Exploring the equivalence of two common mixture models for duration data. The American Statistican, 73 (3). pp. 288-295. ISSN 0003-1305


The beta-geometric (BG) distribution and the Pareto distribution of the second kind (P(II)) are two basic models for duration-time data that share some underlying characteristics (i.e., continuous mixtures of memoryless distributions), but differ in two important respects: first, the BG is the natural model to use when the event of interest occurs in discrete time, while the P(II) is the right choice for a continuous-time setting. Second, the underlying mixing distributions (the beta and gamma for the BG and P(II), respectively, are very different—and often believed to be non-comparable with each other. Despite these and other key differences, the two models are strikingly similar in terms of their fit and predictive performance as well as their parameter estimates. We explore this equivalence, both empirically and analytically, and discuss the implications from both a substantive and methodological standpoint.

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Item Type: Article
Subject Areas: Marketing
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in The American Statistican on 25th March 2019, available online: https://www.tandfonline.com/doi/full/10.1080/00031305.2018.1543134
Subjects: P > Pareto's law
Date Deposited: 13 Nov 2018 16:07
Last Modified: 20 Aug 2019 09:02
URI: http://lbsresearch.london.edu/id/eprint/1027

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