The Pareto distribution is a heavy-tailed distribution with many applications in the real world. The tail of the distribution is\r\nimportant, but the threshold of the distribution is difficult to determine in some situations. In this paper we consider two realworld\r\nexamples with heavy-tailed observations, which leads us to propose a mixture truncated Pareto distribution (MTPD) and\r\nstudy its properties.We construct a cluster truncated Pareto distribution (CTPD) by using a two-point slope technique to estimate\r\nthe MTPD from a random sample.We apply the MTPD and CTPD to the two examples and compare the proposed method with\r\nexisting estimation methods. The results of log-log plots and goodness-of-fit tests show that the MTPD and the cluster estimation\r\nmethod produce very good fitting distributions with real-world data.
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