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題 名 | 統計量的S-系統計算法=On the S-system Computation of Statistical Distributions |
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作 者 | 陳仁義; 陳建中; 賴振耀; | 書刊名 | 中國統計學報 |
卷 期 | 37:3 1999.09[民88.09] |
頁 次 | 頁219-240 |
分類號 | 314.22 |
關鍵詞 | 泰勒式; 統計計算; 演算法; 微分方程; 冪次律; 轉化; Differential equation; Power law; Recasting; Statistical computing; Taylor series; |
語 文 | 中文(Chinese) |
中文摘要 | s-系統(S-Syystem)是從生物學、免疫學和生物化學等領域中發展出來的,其標 準式為非線性多元常微分方程式組所形成的系統其中Xi=dXi/dt,αi和βi 比為非負的實 數,而 gij 和 hij 則是任何的實數。本文針對 S- 系統的數值計算方法做進一步地探討, 提出有效率的步長控制法和截泰勒式之階次詞整方式,並應用於常用統計亡的計算; 與現有 的封閉型數值計算軟體 ESSYNS 作比較,我們的執行結果明碩地較能達到預期的準確度。 |
英文摘要 | Many well-known statistical distributions can be recast in the S-system form of a set of simultaneous nonlinear first-order differential equations. The canonical form of S-System is represented as where Xi = dXi/dt,αi and βi are nonnegative, and gij and hij are any real numbers. In this article, the numerical methods of S-system formulation are further studied on the basis of Irvine and Savageau (1990). The adaptive methods to adjust the step size and the order of approximated Taylor's series in the proceeding of numerical computing are proposed and applied to computing and evaluating various distributionaJ densities, cumulatives, and quantiles. In comparison with the package ESSYNS, our modified algorithm for S-system formulation shows notable numerical improvement. |
本系統中英文摘要資訊取自各篇刊載內容。