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would reduce far less over the last century, if at all.

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Halley 1687-1691 Sweden 1754-1756 Switzerland 1876-1880 Japan 1950-1954 Japan 1980-1984 Japan 2000-2004 Fries (1980)

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The figure above, reproduced from the paper by Robine, et al., demonstrates the non-normal symmetry of the distribution of deaths for actual records versus that hypothesized by Fries. The illustration is particularly interesting for the change in Japanese mortality between 1982 and 2002, when the mode and the distribution above shifted to the right, but the distribution below the mode effectively stretched rather than shifted. Robine et al. observed that for the United States, the standard deviation above the mode has been “roughly constant” over longer periods, unlike most other countries. In fact this observed behavior for the United States, once thought to be an aberration, may have been a predictor for Japan since 1982 and for other countries in the future. Thus, the United States for some time, and now Japan since 1982, seem to be demonstrating resistance to further mortality compression above the modal age at death.

Given the clear fact that the distribution by age at death is not normal and is apparently not moving in that direction, additional measures are worth study. It would be useful in this analysis to consider changes in the mean and the mode simultaneously. If

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