### Mortality by the book

#### (Dec 22, 2017)

Our book, Modelling Mortality with Actuarial Applications, will appear in Spring 2018.  I wrote the second of the three parts, where I describe the modelling and forecasting of aggregate mortality data, such as provided by the Office for National Statistics, the Human Mortality Database or indeed by any insurer whose own data is suitable.  I have divided my contribution into four chapters. In the first chapter I deal with one-dimensional data, for example, deaths by age for a given year.  The Gompertz model is used to introduce the regression-based approach; estimation is initially by least squares, but by the end of the chapter I use generalized linear models (GLMs) with both Poisson and binomial errors.

Tags: GLMs, mortality projections, R

### Quantiles and percentiles

#### (Aug 20, 2014)

Quantiles are points taken at regular intervals from the cumulative distribution function of a random variable. They are generally described as q-quantiles, where q specifies the number of intervals which are separated by q−1 points. For example, the 2-quantile is the median, i.e. the point where values of a distribution are equally likely to be above or below this point.

A percentile is the name given to a 100-quantile.  In Solvency II work we most commonly look for the 99.5th percentile, i.e. the point at which the probability that a random event exceeds this value is 0.5%.  The simplest approach to estimating the 99.5th percentile might be to simulate 1,000 times and take the 995th or 996th largest…

Tags: quantile, percentile, Solvency II, Excel, R