The aggregate loss model has applications in various areas such as financial
risk management and actuarial science. The aggregate loss is the summation of all
random losses occurred in a period. While the impact of the loss severity on aggregate loss is well studied,
less focus is paid on the influence of loss frequency on aggregate loss, which motivates
our study. We enrich the aggregate loss framework by introducing the
Poisson-Tweedie distribution as a candidate for modelling loss frequency, prove the
closedness of Poisson-Tweedie under binomial-thinning, investigate bias of parameter
and quantile estimation through simulation and apply our proposed model on Transportation Security Administration (TSA)
Claims data to demonstrate its application. The Poisson-Tweedie distribution family contains many
of the commonly used distributions for modelling loss frequency, thus making loss
frequency fitting more flexible and reduce the chance of model misspecification.