## Bootstrapping Parametric Models of Mortality

**Abstract :**
We consider a general problem of modeling a mortality law
of a population of failing units
with some parametric function. In this setting we define a mortality
table of crude rates as
a statistical estimator with multinomial distribution and show its
consistency as well as asymptotic
normality. We further derive the statistical properties of parameter
estimators in a parametric mortality model based on a weighted
square loss function. We use the
obtained results to study consistency and appropriateness of the
parametric bootstrap method in our setting.
We derive the conditions on the assumed
parametric mortality law and the loss
function, under which the bootstrap is consistent for estimating the
model parameters, their standard
errors and corresponding confidence intervals. We apply our results
to a model of Aggregate US Mortality
Table based on a so called mixture of extreme value distributions
suggested by Carriere (1992).