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On Selecting a Spurious Observation

Published online by Cambridge University Press:  20 November 2018

K. S. Mount  and
B. K. Kale
K. S. Mount
Affiliation:
University of Manitoba, Winnipeg Manitoba
B. K. Kale
Affiliation:
University of Manitoba, Winnipeg Manitoba
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Consider a life testing experiment in which (Xl, X2,…,Xn) are such that (n—1) of them are distributed as f(x, σ)=(l/σ)e-x/σ, x ≥ σ, > 0 and one of them is distributed as f(x, σ/α), 0 < α< l. A priori each Xi has probability 1/n of being a spurious observation distributed as f (x,σ/α). For such an experiment Kale and Sinha [2] showed that if ur denotes the probability that X(r), the rth component of the order statistic, corresponds to the spurious observation, then u1 < u2 < … < un.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 75 - 78
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Ferguson, T., Mathematical statistics, a decision theoretic approach, Academic Press, 1967.Google Scholar
2. Kale, B. K., and Sinha, S. K., Estimation of expected life in the presence of an outlier observation. Technometrics, 13 (1971), 755–759.Google Scholar
3. Lehmann, E. L., Testing statistical hypotheses, Wiley, New York, 1959.Google Scholar