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Sequential Estimation in Exponential Distribution
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 Title & Authors
Sequential Estimation in Exponential Distribution
Park, Sang-Un;
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 Abstract
In this paper, we decompose the whole likelihood based on grouped data into conditional likelihoods and study the approximate contribution of additional inspection to the efficiency. We also combine the conditional maximum likelihood estimators to construct an approximate maximum likelihood estimator. For an exponential distribution, we see that a large inspection size does not increase the efficiency much if the failure rate is small, and the maximum likelihood estimator can be approximated with a linear function of inspection times.
 Keywords
Conditional likelihood;Fisher information;life testing;maximum likelihood estimator;order statistics;
 Language
English
 Cited by
 References
1.
Gersbakh, I. (1995). On the Fisher information in the Type-I censored and quantal response data. Statistics and probability Letters, 23, 297-306 crossref(new window)

2.
Kendell, P. J. and Anderson, R. L. (1971). An estimation problem in life-testing. Technometrics, 13, 289-301 crossref(new window)

3.
Kulldorff, G. (1961). Estimation from Grouped and Partially Grouped Samples. John Wiley & Sons, New York

4.
Meeker, W. Q. (1986). Planning life tests in which units are inspected for failure. IEEE Transactions on Reliability, 35, 571-578 crossref(new window)

5.
Nelson, W. (1977). Optimum demonstration tests with grouped inspection data from exponential distribution. IEEE Transactions on Reliability, 36, 226-231

6.
Nelson, W. (1982). Applied Life Data Analysis. John Wiley & Sons, New York

7.
Park, S. (1996). An asymptotic relation arising in the decomposition of the likelihood of order statistics. Statistics and Probability Letters, 29, 101-106 crossref(new window)

8.
Park, S. (2003). On the asymptotic Fisher information in order statistics. Metrika, 57, 71-80 crossref(new window)

9.
Park, S. and Kim, C. E. (2006). A note on the Fisher information in exponential distribution. Communications in Statistics: Theory and Methods, 35, 13-19 crossref(new window)

10.
Seo, S. and Yum, B. (1993). Estimation methods for the mean of the exponential distribution based on grouped and censored data. IEEE Transactions on Reliability, 42, 87-96 crossref(new window)

11.
Shapiro, S. S. and Gulati, S. (1996). Selecting failure monitoring times for an exponential life distribution. Journal of Quality Technology, 28, 429-438

12.
Sukhatme, P. V. (1937). Tests of significance for samples ofthe $X^2$ population with two degrees of freedom. Annals of Eugenics, 8, 52-56 crossref(new window)

13.
Tallis, G. M. (1967). Approximate maximum likelihood estimates from grouped data. Technometrics, 9, 599-606 crossref(new window)

14.
Zheng, G. and Gastwirth, J. L. (2000). Where is the Fisher information in an ordered sample? Statistica sinica, 10, 1267-1280