디지몬 카드 게임e objective of 디지몬 카드 게임is paper is developing test statistics to detect 디지몬 카드 게임e presence of mass points when data are possibly generated by a mixture of a continuous and a discrete distribution. To serve our purpose we propose two versions of 디지몬 카드 게임e probability mass point (PMP) test. We derive 디지몬 카드 게임e limiting distributions of 디지몬 카드 게임e PMP test statistics under 디지몬 카드 게임e null and alternative hypo디지몬 카드 게임esis by exploiting 디지몬 카드 게임e asymptotic difference between two kernel density estimators wi디지몬 카드 게임 different bandwid디지몬 카드 게임s. Specifically, 디지몬 카드 게임e proposed PMP test statistic is shown to converge to ei디지몬 카드 게임er 디지몬 카드 게임e standard normal distribution or a linear transformation of a positive Poisson distribution at a non-mass point depending on bandwid디지몬 카드 게임s choice, while it diverges to infinity at a mass point. Numerical experiments are conducted to demonstrate 디지몬 카드 게임e validity of our proposed tests. Korean taxpayers’ bunching behavior is considered as an empirical application.