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Extremes are not normal: a reminder to demographers

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Abstract

Demographers have always held great interest in extremal phenomena. Extreme value distributions are tailor made to model extremes but demographers do not often take advantage of them. We argue that demographers would benefit by using these models more often and present one potential usage: the Extreme Value Distribution as a candidate for modelling the error distribution in time series models. As an example, we use the so called best practice life expectancy. The residuals from the fitted models are tested for Normality. They are also fitted with Gaussian and Generalized Extreme Value distributions and the fit of these two distributions is compared. The results suggest that demographers ought to further explore and take greater advantage of extreme value models.

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Authors and Affiliations

  1. Center on Population Dynamics, University of Southern Denmark, Odense, Denmark

    Anthony Medford & James W. Vaupel

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  1. Anthony Medford
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  2. James W. Vaupel
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Correspondence to Anthony Medford.

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Appendices

Appendix 1: Diagnostics for differenced residuals

See Figs. 2, 3, 4 and 5.

Fig. 2
figure 2

Diagnostics for differenced residuals for data period beginning in 1950

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Fig. 3
figure 3

Diagnostics for differenced residuals for data period beginning in 1960

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Fig. 4
figure 4

Diagnostics for differenced residuals for data period beginning in 1970

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Fig. 5
figure 5

Diagnostics for differenced residuals for data period beginning in 1980

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Appendix 2: Diagnostics for detrended residuals

See Figs. 6, 7, 8 and 9.

Fig. 6
figure 6

Diagnostics for detrended residuals for data period beginning in 1950

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Fig. 7
figure 7

Diagnostics for detrended residuals for data period beginning in 1960

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Fig. 8
figure 8

Diagnostics for detrended residuals for data period beginning in 1970

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Fig. 9
figure 9

Diagnostics for detrended residuals for data period beginning in 1980

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Medford, A., Vaupel, J.W. Extremes are not normal: a reminder to demographers. J Pop Research 37, 91–106 (2020). https://doi.org/10.1007/s12546-019-09231-y

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  • DOI: https://doi.org/10.1007/s12546-019-09231-y

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