Forecasting Age Distribution of Deaths: Cumulative Distribution Function Transformation

TL;DR

This paper introduces a cumulative distribution function transformation method for forecasting age-specific death counts from life tables, improving accuracy over existing compositional data approaches and aiding demographic and actuarial applications.

Contribution

The paper presents a novel CDF transformation approach for forecasting life-table death counts that respects their nonlinear constraints, outperforming existing methods.

Findings

The proposed method yields more accurate point forecasts.

It provides better interval forecast coverage.

It enhances estimation of survival probabilities and life expectancy.

Abstract

Like density functions, period life-table death counts are nonnegative and have a constrained integral, and thus live in a constrained nonlinear space. Implementing established modelling and forecasting methods without obeying these constraints can be problematic for such nonlinear data. We introduce cumulative distribution function transformation to forecast the life-table death counts. Using the Japanese life-table death counts obtained from the Japanese Mortality Database (2024), we evaluate the point and interval forecast accuracies of the proposed approach, which compares favourably to an existing compositional data analytic approach. The improved forecast accuracy of life-table death counts is of great interest to demographers for estimating age-specific survival probabilities and life expectancy and actuaries for determining temporary annuity prices for different ages and maturities.