This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.

The world population is aging, which along with recent shifts in the labor force participation (LFP), is having a significant longevity influence on state pension programs across the board, including Canada, Finland, Japan, and Germany. Except Japan, these countries have set their statutory re-tirement age at 65, but the impact of aging workforce and declined fertility rates create wonders on the estimate future trends in the LFP, as well as the length of retirement. In this study, we fit the LFP rates of these countries, representing continents from Asia, Europe and North America among the OECD countries, using the Lee-Carter and Cairns-Blake-Dowd (CBD) stochastic models. The es-timates are then used for the projection of future LFP rates (1989-2066), and by combining the mortality forecasts from the United Nations, we project the expected length of retirement (1989-2066). This study provided a novel comparison between the Lee-Carter and the CBD LFP models by fitting and forecasting the LFP rates of senior employees between 50- to 74-year-olds. The results revealed disparities between models that provided proof of the presence of model risk for longer retirement durations. The study findings emphasized the importance for decision-makers in pension industry to have awareness of potential risks and limits associated with the LFP models. The Lee-Carter model outperformed the CBD model even though the CBD model is known for its ac-curate prediction in higher ages. Population aging should be considered in any analysis of the long-term viability of pensions, together with the participation rate trends for a sustainable labor market future.

The ageing global population and changing labor force participation are having a profound impact on state pension programs worldwide, including Malaysia. However, the effects of an ageing workforce and declining fertility rates are having a significant impact on future trends in labor force participation and the duration of retirement. This paper presents an innovative examination of labor force participation rate (LFPR) forecasting within the context of an aging workforce, utilizing the Lee-Carter and Cairns-Blake Dowd stochastic models, traditionally applied to mortality data. By adapting these models to LFPR data, the study offers a novel perspective on predicting workforce participation trends and understanding the dynamics of retirement planning from year 2001 to 2047. Additionally, by incorporating the mortality forecasts from the United Nations, the research navigates through the complexities of applying actuarial methods to labor economics, revealing differentiated pathways for male and female participation in the labor market and the anticipated length of retirement. This study offers a unique comparison between the Lee-Carter and the Cairns-Blake-Dowd (CBD) LFPR models. It focuses on fitting and forecasting the LFPR of senior employees aged 50 to 64. The results highlighted discrepancies among models that demonstrated evidence of model risk for extended retirement duration.