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Mortality convergence

In his blog on socio-economic differentials in England and Wales, Torsten Kleinow showed how mortality rates between sub-groups converge with age. And in his blog on ill-health retirements, Kai Kaufhold demonstrated how excess mortality relative to normal retirements reduces, then vanishes.
Written by: Stephen RichardsTags: mortality convergence, compensation law of mortality, mortality plasticity

Auditing firewalls

In a recent blog I discussed the security improvements brought by changing our certification authority, but that isn't our only recent change.
Written by: Gavin RitchieTags: technology, defence in-depth

Fun and games with constraints

I'm a statistician so I worry about standard errors just as much as I worry about point estimates. My blog Up close and intimate with the APCI model looked at the effect of different constraints on parameter estimates in models of mortality. This blog looks at the effect of constraints on the standard errors of the parameter estimates.

Written by: Iain CurrieTags: constraints, identifiability

Resetting certificates

Web site certification supports the key exchange enabling secure encrypted communication between browser clients and server applications. This is why industry giant Google launched a campaign in 2014 that all web applications should use a browser-recognised certificate authority (CA) and offer encrypted access.
Written by: Gavin RitchieTags: technology, defence in-depth

Seasonal mortality and age

In two previous blogs (here and here) I looked at excess winter mortality.  A first glance at the charts shows that the elderly dominate the death counts.  However, the elderly also happen to provide the bulk of deaths at any time of year, so how can we be sure that they are more vulnerable to seasonal variation?
Written by: Stephen RichardsTags: season, winter

The Hermite model of mortality

In Richards (2012) I compared seventeen different parametric models for modelling the mortality of a portfolio of UK annuitants. The best-fitting model, i.e. the one with the lowest AIC, was the Makeham-Beard model:

\[\mu_x = \frac{e^\epsilon+e^{\alpha+\beta x}}{1+e^{\alpha+\rho+\beta x}}\qquad(1)\]

Written by: Stephen RichardsTags: Hermite splines, extrapolation

The Poisson assumption under the microscope

If you read almost any paper on modelling mortality you will find the assumption that the number of deaths follows the Poisson distribution.
Written by: Iain Currie

The cohort effects that never were

The analysis of cohort effects has long fascinated the actuarial community; these effects correspond to the observation that specific generations can have longevity characteristics different from those of the previous and the following ones. However, Richards (2008) conjectured that these cohort effects might be errors caused by sudden changes in fertility patterns.
Written by: Alexandre BoumezouedTags: cohort effect, mortality improvements

Mortality down under

Different countries have different mortality characteristics, and this is true even where countries have similar levels of wealth and development.  However, different countries also have shared mortality characteristics, and one of these is seasonal variation. 
Written by: Stephen RichardsTags: season, winter, cause of death

Is your mortality model frail enough?

Mortality at post-retirement ages has three apparent stages:

  1. A broadly Gompertzian pattern up to age 90 (say), i.e. the mortality hazard is essentially linear on a logarithmic scale.

  2. The rate of increase in mortality slows down, the so-called "late-life mortality deceleration".

Written by: Stephen RichardsTags: late-life mortality deceleration, frailty, heterogeneity