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Modeling Best Practice Life Expectancy Using Gumbel Autoregressive Models

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  • Anthony Medford

    (Interdiscliplinary Centre on Population Dynamics, University of Southern Denmark, 5000 Odense C, Denmark)

Abstract

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best practice life expectancy. This class of model represents a neat and coherent framework for modeling time series extremes. The Gumbel distribution accounts for the extreme nature of best practice life expectancy, while the AR structure accounts for the temporal dependence in the time series. Model diagnostics and simulation results indicate that these models present a viable alternative to Gaussian AR(1) models when dealing with time series of extremes and merit further exploration.

Suggested Citation

  • Anthony Medford, 2021. "Modeling Best Practice Life Expectancy Using Gumbel Autoregressive Models," Risks, MDPI, vol. 9(3), pages 1-10, March.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:3:p:51-:d:514193
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    References listed on IDEAS

    as
    1. Jackie Li & Jia Liu, 2020. "A modified extreme value perspective on best-performance life expectancy," Journal of Population Research, Springer, vol. 37(4), pages 345-375, December.
    2. Jacques Vallin & France Meslé, 2009. "The Segmented Trend Line of Highest Life Expectancies," Population and Development Review, The Population Council, Inc., vol. 35(1), pages 159-187, March.
    3. Anthony Medford & James W. Vaupel, 2020. "Extremes are not normal: a reminder to demographers," Journal of Population Research, Springer, vol. 37(1), pages 91-106, March.
    4. Anne‐Laure Fougères & John P. Nolan & Holger Rootzén, 2009. "Models for Dependent Extremes Using Stable Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 42-59, March.
    5. Martin Crowder, 1998. "A Multivariate Model for Repeated Failure Time Measurements," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 53-67, March.
    6. Anthony Medford, 2017. "Best-practice life expectancy: An extreme value approach," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 36(34), pages 989-1014.
    7. Jia Liu & Jackie Li, 2019. "Beyond the highest life expectancy: construction of proxy upper and lower life expectancy bounds," Journal of Population Research, Springer, vol. 36(2), pages 159-181, June.
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