A Bayesian Gamma Frailty Model Using the Sum of Independent Random Variables: Application of the Estimation of an Interpurchase Timing Model

Ryosuke Igari and Takahiro Hoshino
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Ryosuke Igari: Faculty of Business Administration, Hosei University

No 2018-021, Keio-IES Discussion Paper Series from Institute for Economics Studies, Keio University

Abstract: In statistics, researchers have rigorously investigated the reproductive property, which maintains that the sum of independent random variables with the same distribution follows the same family of distributions. However, even if a distribution of the sum of random variables demonstrates the reproductive property, estimating parameters appropriately from only summed observations is difficult. This is because of identification problems when component random variables have different parameters. In this study, we develop a method to effectively estimate parameters from the sum of independent random variables with different parameters. In particular, we focus on the sum of Gamma random variables composed of two types of distributions. We generalize the result according to Moschopoulos(1985) to a proportional hazard model with covariates and a frailty model to capture individual heterogeneities. Additionally, to estimate each parameter from the sum of random variables, we incorporate auxiliary information using quasi-Bayesian methods, and we propose the estimation procedure by Markov chain Monte Carlo. We confirm the effectiveness of the proposed method through a simulation study and apply it to the interpurchase timing model in marketing.

Keywords: Survival Analysis; Random Effects; Auxiliary Information; Quasi-Bayesian Inference; Markov Chain Monte Carlo (search for similar items in EconPapers)
JEL-codes: C11 C41 M31 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2018-12-17
New Economics Papers: this item is included in nep-ecm, nep-mkt and nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:keo:dpaper:2018-021

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