The year 2025 marks the 200th anniversary of the publication of Benjamin Gompertz’s law of mortality. At that time, the computation of an annuity premium required the use of logarithmic tables, and deriving analytical formulas for quantities such as the modal age at death or the mean age at death was out of reach. More than one hundred years later, Emil Gumbel introduced what is now known as the Gumbel distribution. When accumulated from the lowest to the highest values, this distribution leads to extreme value theory; when accumulated from the highest to the lowest values, it yields the survival function of the Gompertz law of mortality.
Nicolas Brouard (Wed,) studied this question.