1. NCCU Academic Hub
  2. Publications
  3. College of Commerce
  4. Theses
  5. Item

Publications-Theses

Article View/Open

Publication Export

Google ScholarTM

NCCU Library

Citation Infomation

Related Publications in TAIR

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-May-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 (Authors) 吳碩傑zh_TW
dc.creator (作者) 吳碩傑zh_TW
dc.date (日期) 1989en_US
dc.date.accessioned 4-May-2016 14:24:01 (UTC+8)-
dc.date.available 4-May-2016 14:24:01 (UTC+8)-
dc.date.issued (上傳時間) 4-May-2016 14:24:01 (UTC+8)-
dc.identifier (Other Identifiers) B2002005727en_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/#B2002005727en_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 Distributionen_US
dc.type (資料類型) thesisen_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