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題名 有關預測柏拉圖母體之樣本觀測值的研究
The Prediction Problems of Sample Observations for Pareto Distribution作者 吳碩傑 貢獻者 歐陽良裕
吳碩傑日期 1989 上傳時間 4-五月-2016 14:24:01 (UTC+8) 摘要 論文摘要 在有關產品可靠度問題之研究中，通常需要做產品抽樣壽命試驗。由於壽命試驗一一般屬於破壞性試驗，且費時頗久，成本支出甚鉅。因此，如何快速且有效地得到試驗結果，以作為評估及改善產品可靠度的依據，並供決策參考，便極為重要。 本文討論在母體壽命為柏拉圖分布時，研究如何以早期發生故障之樣本壽命觀測值來求得其後發生故障之樣本觀測值的點預測及區間預測。 參考文獻 [1] Draper, N. R. and Smith, H. (1981). Applied Regression Analysis. 2nd. Ed., John Wiley & Sons, New York. [2] Engelhardt, M., Bain, L. J., & Shiue, Wei-Kei (1986). Statistical Analysis of a compound exponential failure model. Journal of Statistical Computation and Simulation, Vol.23, pp 299-315. [3] Goldberger, A. S. (1962). Best linear unbiased prediction in the generalized lineap regression model. Journal of American Statistical Association, Vol. 57, pp 369-375. [4] Graybill, F. A. (983). Matrices with Applications in Statistics. 2nd. Ed. Wadsworth, Belmont, CA. [5] Kaminsky, K. S., Mann, N. R., & Nelson, P. 1. (975). Best and simplified linear invariant prediction of order statistics in location and scale families. Biometrika, Vol. 62, pp 525-527. [6] Kaminsky, K. S. and Nelson, P. 1. (975). Best linear unbiased prediction of order statistics in location and scale families. Journal of American Statistical Association, Vol. 70, pp 145-150. [7] Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York. [8] Lloyd, E. H. (1952). Least-squares estimation of location and scale parameters using order statistics. Biometrika, Vol. 39. pp 88-95. [9] Mann, H. R. (1969). Optimum estimators for linear functions of location and scale parameters. Annals of Mathematical Statistics, Vol. 40, pp 2149-2155. [10] Mann, N. R., Schafer, R. E., & Singpurwalla, N. D. (974). Methods for Statjstical Analysjs of Reljability and Life Data. John Wiley & Sons, New York. [11] Munro, A. H. and Wixley, R, A. J. (970). Estimators based OD order statistics of small samples from a three-parameter lognormal distribution. Journal of American Statistical Association, Vol. 65. pp 212-225. [12] Nelson, W. and Schmee, J. (1981). Predition limits for the last failure time of a (log) normal sample from early failures. IEEE Transactions on Reliability, Vol. R-30, pp 461-463. [13] Pyke, R. (1965). Spacings. Journal of the Royal Statistical Society Series B, Vol. 27, pp 395-449 (with discussion ). [14] Vannman, K. (1976). Estimators based on order statistics from a Pareto distribution. Journal of American Statistical Association. Vol. 71, pp 704-708. [15] Wingo, D. R. (1982). Unimodality of the Pareto distribution likelihood function for multicensored samples and implications for estimations. Communications in Statistics －Theory and Methods. Vol. 11, pp 1129-1138. 描述 碩士
國立政治大學
統計學系資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002005727 資料類型 thesis dc.contributor.advisor 歐陽良裕 zh_TW dc.contributor.author (作者) 吳碩傑 zh_TW dc.creator (作者) 吳碩傑 zh_TW dc.date (日期) 1989 en_US dc.date.accessioned 4-五月-2016 14:24:01 (UTC+8) - dc.date.available 4-五月-2016 14:24:01 (UTC+8) - dc.date.issued (上傳時間) 4-五月-2016 14:24:01 (UTC+8) - dc.identifier (其他 識別碼) B2002005727 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/90493 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description.abstract (摘要) 論文摘要 在有關產品可靠度問題之研究中，通常需要做產品抽樣壽命試驗。由於壽命試驗一一般屬於破壞性試驗，且費時頗久，成本支出甚鉅。因此，如何快速且有效地得到試驗結果，以作為評估及改善產品可靠度的依據，並供決策參考，便極為重要。 本文討論在母體壽命為柏拉圖分布時，研究如何以早期發生故障之樣本壽命觀測值來求得其後發生故障之樣本觀測值的點預測及區間預測。 zh_TW dc.description.tableofcontents 目錄 第一章 緒論……1 第一節 研究的動機與目的……1 第二節 研究範圍及限制……1 第三節 本文架構……2 第二章 柏拉圖分布參數的估計……5 第一節 最大概似估計式……5 第二節 一般化線性迴歸模式的建立……7 第三節 最佳線性不偏估計式……12 第四節 最佳線性不變估計式……16 第三章 樣本觀測值的點預測……22 第一節 樣本觀測值的最佳線性不偏點預測……22 第二節 樣本觀測值的最佳線性不變點預測……29 第三節 樣本觀測值的終極線性不偏點預測……35 第四章 樣本觀測值的區間預測……39 第一節 樣本觀測值的單邊區間預測……39 第二節 樣本觀測值的近似區間預測……45 第五章 結論……51 附表一 柏拉圖分布A1值B1值及順序統計量期望值……53 附表二 柏拉圖順序統計量共變異數……55 附表三 柏拉圖分步位置參數及尺度參數之BLUE的係數……62 附表四 U=(X(S)-X(K) /σ^之分位數u(δ;n,s,k,λ) ……77 參考文獻……83 附錄一……85 附錄二……99 附錄三……101 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002005727 en_US dc.title (題名) 有關預測柏拉圖母體之樣本觀測值的研究 zh_TW dc.title (題名) The Prediction Problems of Sample Observations for Pareto Distribution en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Draper, N. R. and Smith, H. (1981). Applied Regression Analysis. 2nd. Ed., John Wiley & Sons, New York. [2] Engelhardt, M., Bain, L. J., & Shiue, Wei-Kei (1986). Statistical Analysis of a compound exponential failure model. Journal of Statistical Computation and Simulation, Vol.23, pp 299-315. [3] Goldberger, A. S. (1962). Best linear unbiased prediction in the generalized lineap regression model. Journal of American Statistical Association, Vol. 57, pp 369-375. [4] Graybill, F. A. (983). Matrices with Applications in Statistics. 2nd. Ed. Wadsworth, Belmont, CA. [5] Kaminsky, K. S., Mann, N. R., & Nelson, P. 1. (975). Best and simplified linear invariant prediction of order statistics in location and scale families. Biometrika, Vol. 62, pp 525-527. [6] Kaminsky, K. S. and Nelson, P. 1. (975). Best linear unbiased prediction of order statistics in location and scale families. Journal of American Statistical Association, Vol. 70, pp 145-150. [7] Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York. [8] Lloyd, E. H. (1952). Least-squares estimation of location and scale parameters using order statistics. Biometrika, Vol. 39. pp 88-95. [9] Mann, H. R. (1969). Optimum estimators for linear functions of location and scale parameters. Annals of Mathematical Statistics, Vol. 40, pp 2149-2155. [10] Mann, N. R., Schafer, R. E., & Singpurwalla, N. D. (974). Methods for Statjstical Analysjs of Reljability and Life Data. John Wiley & Sons, New York. [11] Munro, A. H. and Wixley, R, A. J. (970). Estimators based OD order statistics of small samples from a three-parameter lognormal distribution. Journal of American Statistical Association, Vol. 65. pp 212-225. [12] Nelson, W. and Schmee, J. (1981). Predition limits for the last failure time of a (log) normal sample from early failures. IEEE Transactions on Reliability, Vol. R-30, pp 461-463. [13] Pyke, R. (1965). Spacings. Journal of the Royal Statistical Society Series B, Vol. 27, pp 395-449 (with discussion ). [14] Vannman, K. (1976). Estimators based on order statistics from a Pareto distribution. Journal of American Statistical Association. Vol. 71, pp 704-708. [15] Wingo, D. R. (1982). Unimodality of the Pareto distribution likelihood function for multicensored samples and implications for estimations. Communications in Statistics －Theory and Methods. Vol. 11, pp 1129-1138. zh_TW
