We consider a compositional data analysis approach to forecasting the age distribution of death counts. Using the age-specific period life-table death counts in Australia obtained from the Human Mortality Database, the compositional data analysis approach produces more accurate 1- to 20-step-ahead point and interval forecasts than Lee–Carter method, Hyndman–Ullah method and two naïve random walk methods. The improved forecast accuracy of period life-table death counts is of great interest to demographers for estimating survival probabilities and life expectancy, and to actuaries for determining temporary annuity prices for various ages and maturities. Although we focus on temporary annuity prices, we consider long-term contracts that make the annuity almost lifetime, in particular when the age at entry is sufficiently high.

Holmes and Anderson (2017a) introduce two extensive data sets on world alcohol consumption and expenditure and with them investigate, among other things, the possible convergence of national alcohol consumption patterns using wine, beer, and spirit shares. Such share data define a composition, on which conventional statistical analysis using covariances and correlations is invalid. This note reanalyses the data using techniques appropriate for a composition and introduces a statistic that can validly track the variation in national shares around the global mean through time. This variability statistic shows that such convergence of national alcohol patterns has clearly taken place over the period 1961 to 2014 and thus confirms Holmes and Anderson's findings using a valid statistical approach. (JEL Classifications: C18, D12, L66)

Estimates of particle-size made by operators in the field and laboratory represent a vast and relatively untapped data archive. The wide spatial distribution of particle-size estimates makes them ideal for constructing geological models and soil maps. This study uses a large data set from the Netherlands (n = 4837) containing both operator estimates of particle-size and complete particle-size distributions measured by laser granulometry. Operator estimates are inaccurate and imprecise relative to measured laser data; only 16.68% of samples were successfully classified using the Dutch classification scheme for fine sediment. Operator estimates of sediment particle-size encompass the same range of percentage values as particle-size distributions measured by laser analysis. However, the distributions measured by laser analysis show that most of the sand percentage values lie between 0 and 1, so the majority of the variability in the data is lost because operator estimates are made to the nearest 1% at best, and more frequently to the nearest 5%. Operator estimates made by three technicians trained by the Geological Survey of the Netherlands are found not to be influenced by bias, rather they exhibit very similar levels of accuracy and precision. This study compares five different methods of modelling complete particle-size distributions from sparse data: (i) a four-part Pearson's probability distribution function, (i) a log-linear interpolation, (iii) a logit-linear interpolation, (iv) a logistic probability distribution function and (v) a logit constrained cubic-spline (logit-CCS) interpolation. The logit-CCS interpolation performed best across all the samples used, although the performance of all models was very similar for normal Gaussian, skewed and peaked distributions. Predictions for bimodal distributions using the Pearson's, logit-linear and logistic models are markedly less accurate than both log-linear and logit-CCS interpolation models. Although the logit-CCS interpolation model produces the best predictions of continuous particle-size distributions, the low accuracy and precision of operator estimates does not warrant the use of such a complex algorithm. Given this, it is suggested that a standard log-linear interpolation is the most effective means of modelling complete particle-size distributions from sparse data. Interpolation-based models are recommended over probability distribution functions because they allow for a greater degree of flexibility and will always honour the available input data.