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研究生:黃志銘
研究生(外文):Z.M. Huang
論文名稱:二維度逆高斯模型
論文名稱(外文):Bivariate Inverse Gaussian Model
指導教授:李昭勝李昭勝引用關係洪慧念洪慧念引用關係
指導教授(外文):Jack.C.LeeHui-Nien Hung
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:英文
論文頁數:39
中文關鍵詞:逆高斯貝氏先驗分配後驗分配
外文關鍵詞:Inverse GaussianBayesianprior distributionposterior distribution
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本論文是使用二維度逆高斯的模型在我們已經知道某件物品已損害某些百分比後來預估此物的壽命,以及使用最大概似法和貝氏觀點對參數做估計。

In this paper, we are interested in the prediction for the life time
of some objects when we already know those objects have brokenδ percent
via a Bivariate Inverse Gaussian distribution. Parameter estimatation is
also discussed from maximum likelihood and Bayesian points of view.

1 Introduction 1
2 Classical approach to estimation of parameter: 5
2.1 The Probability Density Function of Bivariate Inverse Gaussian 5
2.2 Maximum Likelihood Estimators 7
3 Bayesian Inference 8
3.1 On the Choice of a prior distribution 8
3.1.1 Prior I 8
3.1.2 Prior II 10
3.1.3 Prior III 11
3.1.4 Prior IV 13
3.2 Prediction Inference 16
3.3 Example 19
4 Concluding Remarks 33
Appendix 34
Reference 38

1 Banerjee, A. K., and Bhattacharyya, G. K. (1979). Bayesian
results for the inverse Gaussian distribution with an application.
Technometrics, 21, 247-251.
2 Bhattacharyya, G. K.(1982). Fatigue failure
models-Birnbaum-Saunders vs. inverse Gaussian.IEEE Trans. Reliab.
R-31(5):439-440.
3 Bhattacharyya (1976). A purchase incidence model with
inverse Gaussian interpurchase times. J. Amer. Statist. Assoc. 71,
823-829.
4 B. Betro and Rotondi R.(1991).On Bayesian inference for the
Inverse Gaussian distribution.Statistics and Probability Letters 11. 219-224.
5 Chhikara, R. S.(1972). Statistical inference related to the
inverse Gaussian distribution. Ph.D. Dissertation, Oklahoma State
University, Stillwater.
6 Chhikara, R. S. and Folks, J. L.(1974). Estimation of the
inverse Gaussian distribution function. J. Amer. Statist. Ass. 69,
250-254.
7 Chhikara, R.S. and Folks, J.L. (1977). The inverse Gaussian
distribution as a lifetime model. Technometrics 19, 461-468.
8 Chhikara, R. S. and Guttman, I.(1982). Prediction Limits
for the Inverse Gauissian Distribution. {\it Technometrics} , Vol. 24, NO.
4.
9 Lee, J. C. and Tsao, S. L.(1993). On Estimation and Prediction
Procedures for AR(1) Models with Power Transformation. Journal of
Forecasting, Vol. 12, 499-511.
10 Lancaster, A. (1972). A stochastic model for the duration
of a strike. J. R. Statist. Soc. B 135, 257-271.
11 Hasofer, A.M. (1964). A dam with inverse Gaussian inpute.
Proc.Camb. Phil. Sovc. 60, 931-933. J. Amer. Statist. Assoc.
71, 823-829.
12 Sheppard, C.W. (1962). Basic principles of the tracer
thod.New York : Wiely.
13 Tweedie, M. C. K.(1957a). Statistical properties of inverse
ussian distributions I. Ann. Math. Statist.,28:362-377.

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