本論文主要在探討由內往外的序列或連續檢定程序來檢測出雙參數指數樣本中 k 個較大的離群值。我們總共考慮六個檢定統計量，其中一個統計量是根據樣本中可能不被懷疑為離群值的觀測值，計算其中最大觀測值和平均數之間的差與其相對樣本全距之比率；其他五個檢定統計量則是分別在 Basu (1965)、Balasooriya and Gadag (1994)、Zerbet and Nikulin (2003) 和 Kumar (2013b) 的論文中所討論過的區塊檢定程序所使用的統計量。利用Huffer (1988)的遞迴關係式和 Lin and Balakrishnan (2009) 的演算法，我們分別找出以上六個檢定統計量在 k = 2 和 3 時，雙參數指數中 k 個較大的離群值的連續檢定程序之聯合虛無分配的臨界值。最後，再根據蒙地卡羅模擬的方法來比較這六個檢定統計量的檢定力和錯誤判定機率。

The inside-out sequential procedures for testing up to k upper outliers in a two-parameter exponential sample are investigated. Six test statistics, one based on the ratio of the difference of largest observation and the sample mean which are unsuspected to be outliers to the range of these observations, and others used for block test procedures discussed in Basu (1965), Balasooriya and Gadag (1994), Zerbet and Nikulin (2003), and Kumar (2013b), are considered. Utilizing the recursion of Huffer (1988) and algorithm of Lin and Balakrishnan (2009), the critical values of the joint null distributions of these test statistics for sequential testing discordancy of k upper outliers in two-parameter exponential samples on the important cases k = 2 and 3 are obtained. Powers of tests based on these statistics are compared through a Monte Carlo study.

Contents
1 Introduction 1
2 The Distribution of Test Statistics 4
3 Illustrative Examples 6
4 Performance Comparison 10
5 Concluding Remarks 13
References 13
Appendix 16
List of Tables
Table 1 Exact critical values of test statistics (3) to (8) for j = 1, 2, and the associated value of β when α = 0.05. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Table 2 Exact critical values of test statistics (3) to (8) for j = 1, 2, 3, and the associated value of β when α = 0.05. . . . . . . . . . . . . . . . . . . . . . . . . 8
Table 3 Exact critical values of test statistics and the corresponding observed statistics for j = 1, . . . , k when k ≤ 4 in Example 1. . . . . . . . . . . . . . . . . . . 9
Table 4 Exact critical values of test statistics and the corresponding observed statistics for j = 1, . . . , k when k ≤ 4 in Example 2. . . . . . . . . . . . . . . . . . . 11
List of Figures
Figure 1 Powers and error probabilities of testing procedures for n = 10 when k = 2. 20
Figure 2 Powers and error probabilities of testing procedures for n = 15 when k = 2. 21
Figure 3 Powers and error probabilities of testing procedures for n = 20 when k = 2. 22
Figure 4 Powers and error probabilities of testing procedures for n = 15 when k = 3. 23
Figure 5 Powers and error probabilities of testing procedures for n = 30 when k = 3. 24
Figure 6 Powers and error probabilities of testing procedures for n = 50 when k = 3. 25
Figure 7 Powers and error probabilities of testing procedures for n = 100 when k = 3. 26

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