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In a bucket sorting algorithm, the key to increase bucket sorting efficiency is how to uniformly distribute records into each "bucket". The data collected from empirical studies usually follow a certain probability distribution in a certain interval. To sort this kind of data, this paper proposed an innovative method through constructing a hash function based on its probability density function. Then n records can be allocated into n buckets uniformly according to the value of their key, which enables the sorting time of the proposed bucket sorting algorithm to reach O(n) under any circumstance.