Description: The zeta distribution with regression parameters has been rarely used in statistics because of the difficulty of estimating the parameters by traditional maximum likelihood. This is the abstract of a paper that proposes an alternative method for estimating the parameters based on an iteratively reweighted least-squares algorithm.

Description: Logistic-type models for the force of mortality like those introduced by Perks or Kannisto provide better fit to mortality data of people aged over 85 than Makeham’s model where the force of mortality increases exponentially with age. However, the difficulty in estimating their parameters by the maximum likelihood method makes their use less popular among actuaries. For Kannisto’s model, this paper proposes a weighted least-squares estimator which can easily be calculated with any regression software. The estimator is shown to be consistent, asymptotically unbiased and normally distributed. For Perks’ model, using a Taylor’s series expansion, the estimation problem is again reduced to a least-squares problem. The various estimators proposed in the paper are compared numerically using Canadian mortality data.