Kernel type estimator of the mean for a heavy-tailed distribution under random truncation

In this paper, we introduce a kernel estimator designed for estimating the mean of a heavy-tailed distribution under random truncation. The classical estimator for this problem was proposed by (khanssa bendahmane et al , 2021), but it is often limited in its ability to handle the complexities of heavy-tailed distributions. Our proposed kernel estimator addresses these limitations by leveraging kernel smoothing techniques to more accurately estimate the mean under truncation. We derive the asymptotic distributional properties of the new estimator, providing a rigorous mathematical foundation for its performance. In addition, we conduct a simulation study to assess the effectiveness of the estimator. The results of this simulation demonstrate that, compared to the classical estimator, our new approach outperforms it in terms of bias reduction and root mean squared error (RMSE). This highlights the practical advantages of using the kernel estimator, especially in cases involving heavy-tailed distributions where classical methods may be less reliable.