摘 要
這幾年來雙邊冪分配逐漸受到重視，像van Dorp和Kotz（2002a）及Nadarajah（2003）的研究對雙邊冪分配都有詳細的說明。和傳統三角分配相比，雙邊冪分配使用上彈性較大；和Beta分配相比，其機率值的計算比較容易。在討論參數估計的問題時，如van Dorp和Kotz（2002a）及Nadarajah（2003）都假設雙邊的形狀是一樣的，Herrerias,et al.（2009）除了詳細介紹雙邊冪分配的性質之外，也提出一個遞迴求解的方式進行估計。在該篇文章中，也提到雙邊冪分配可以用混合模式來呈現。本文將利用此混合模式建立一雙邊冪分配的演算法，並以數值模擬來說明我們的方式。

Abstract

In recent years, the two sided power distribution is valued gradually. Such as van Dorp, Kotz (2002a) or Nadarajah (2003) detailed the two sided power distribution in their research. Compared with the traditional triangular distribution, using the two sided power distribution is more flexible; and distribution compared with Beta, the calculation of its probability value is easier. In the discussion of parameter estimation, van Dorp, Kotz(2002a) and Nadarajah(2003) assumed that the shape of both sides is equal. The Herrerias,et al.(2009) not only introduced the property of the two sided power distribution in detail, but also propose a algorithm solving approach to estimate. In this article, it also mentioned that the two sided power distribution can be presented by using mixed-model. This article will use the mixed-model to build a two sided power distribution algorithm and explain our ways with the number emulation.

參考文獻

[1] J.R van Dorp and S. Kotz, The standard two sided power distribution and its properties: with applications in financial engineering, Am. Stat. 56 (2) (2002a),
pp. 90-99.

[2] J.R. van Dorp and S. Kotz, A novel extension of the triangular distribution and its parameter estimation, Statistician 56 (2) (2002a), pp. 63-79.

[3] M.A. Johnson and M.R. Taaffe, An investigation of phase-type distribution moment-matching algorithms for use in queuing models, Queuing Syst. 8 (1) (1991), pp. 129-147.

[4] D. Karlis and E. Xekalaki, Improving the EM algorithm for mixtures, Stat. Comput. 9 (4) (1999), pp. 303-307.