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We provide a novel method to analytically calculate the high-order origin moments of a hypergeometric distribution, that is, the expectation identity method. First, the expectation identity of the hypergeometric distribution is discovered and summarized in a theorem. After that, we analytically calculate the first four origin moments of the hypergeometric distribution by using the expectation identity. Furthermore, we analytically calculate the general kth ( k = 1 , 2 , ... ) origin moment of the hypergeometric distribution by using the expectation identity, and the results are summarized in a theorem. Moreover, we use the general kth origin moment to validate the first four origin moments of the hypergeometric distribution. Next, the coefficients of the first ten origin moments of the hypergeometric distribution are summarized in a table containing Stirling numbers of the second kind. Moreover, the general kth origin moment of the hypergeometric distribution by using the expectation identity is restated by another theorem involving Stirling numbers of the second kind. Finally, we provide some numerical and theoretical results. [ABSTRACT FROM AUTHOR]

The bits allocation of video coder using mixed searching MP is proposed and the important ROI regions will be ascertained dynamically during the coding process. Referring to the above results, the original atoms searching scheme will De modified in order to distribute the atoms around the interested regions, thus the reconstructed images' quality of the matching pursuit video coder can De promoted. Experimental results showed that the reconstructed images' quality of the video coder produced by the algorithm accorded well with human subjective conclusion, and the algorithm have desirable application value and low computational cost. [ABSTRACT FROM AUTHOR]