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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-May-2016 14:24:01 (UTC+8)
摘要	論文摘要\r\n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。\r\n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.\r\n[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.\r\n[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.\r\n[4] Graybill, F. A. (983). Matrices with Applications in Statistics. 2nd. Ed. Wadsworth, Belmont, CA.\r\n[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.\r\n[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.\r\n[7] Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York.\r\n[8] Lloyd, E. H. (1952). Least-squares estimation of location and scale parameters using order statistics. Biometrika, Vol. 39. pp 88-95.\r\n[9] Mann, H. R. (1969). Optimum estimators for linear functions of location and scale parameters. Annals of Mathematical Statistics, Vol. 40, pp 2149-2155.\r\n[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.\r\n[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.\r\n[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.\r\n[13] Pyke, R. (1965). Spacings. Journal of the Royal Statistical Society Series B, Vol. 27, pp 395-449 (with discussion ).\r\n[14] Vannman, K. (1976). Estimators based on order statistics from a Pareto distribution. Journal of American Statistical Association. Vol. 71, pp 704-708.\r\n[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)	1989	en_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)	B2002005727	en_US
dc.identifier.uri (URI)	https://ah.lib.nccu.edu.tw/item?item_id=102419	-
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\r\n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。\r\n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\r\n第一章緒論……1\r\n第一節研究的動機與目的……1\r\n第二節研究範圍及限制……1\r\n第三節本文架構……2\r\n第二章柏拉圖分布參數的估計……5\r\n第一節最大概似估計式……5\r\n第二節一般化線性迴歸模式的建立……7\r\n第三節最佳線性不偏估計式……12\r\n第四節最佳線性不變估計式……16\r\n第三章樣本觀測值的點預測……22\r\n第一節樣本觀測值的最佳線性不偏點預測……22\r\n第二節樣本觀測值的最佳線性不變點預測……29\r\n第三節樣本觀測值的終極線性不偏點預測……35\r\n第四章樣本觀測值的區間預測……39\r\n第一節樣本觀測值的單邊區間預測……39\r\n第二節樣本觀測值的近似區間預測……45\r\n第五章結論……51\r\n附表一柏拉圖分布A1值B1值及順序統計量期望值……53\r\n附表二柏拉圖順序統計量共變異數……55\r\n附表三柏拉圖分步位置參數及尺度參數之BLUE的係數……62\r\n附表四 U=(X(S)-X(K) /σ^之分位數u(δ;n,s,k,λ) ……77\r\n參考文獻……83\r\n附錄一……85\r\n附錄二……99\r\n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.\r\n[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.\r\n[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.\r\n[4] Graybill, F. A. (983). Matrices with Applications in Statistics. 2nd. Ed. Wadsworth, Belmont, CA.\r\n[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.\r\n[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.\r\n[7] Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York.\r\n[8] Lloyd, E. H. (1952). Least-squares estimation of location and scale parameters using order statistics. Biometrika, Vol. 39. pp 88-95.\r\n[9] Mann, H. R. (1969). Optimum estimators for linear functions of location and scale parameters. Annals of Mathematical Statistics, Vol. 40, pp 2149-2155.\r\n[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.\r\n[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.\r\n[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.\r\n[13] Pyke, R. (1965). Spacings. Journal of the Royal Statistical Society Series B, Vol. 27, pp 395-449 (with discussion ).\r\n[14] Vannman, K. (1976). Estimators based on order statistics from a Pareto distribution. Journal of American Statistical Association. Vol. 71, pp 704-708.\r\n[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