We extended the candidate pool for modelling the aggregate loss frequency to the three-parameter Poisson-Tweedie (PT) distribution family. With a reporting threshold, small losses will not be observed, thus causing a left-truncation phenomenon where the observed loss frequency is less than the real loss frequency. This raises a new challenge in parameter estimation. We prove that Poisson-Tweedie is closed under binomial thinning. This fact enables us to leverage the existing algorithm for untruncated data to estimate the parameters of the aggregate loss model with truncated data, thus, facilitating the application. With the estimated parameters, the value at risk of the aggregate loss model can be approximated by a Monte-Carlo method. We investigate its application through a simulation study and demonstrate our fitting approach using manual truncation of claims data from the Transportation Security Administration (TSA).