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A new approach to finding sampling distribution for truncated laws. (English) Zbl 1180.62202

Summary: The problem of finding sampling distributions for truncated laws is considered. This problem concerns the very important area of information processing in industrial engineering. It remains today perhaps the most difficult and important of all the problems of mathematical statistics that require considerable efforts and great skill for investigation. The approach discussed here is based on use of the unbiasedness equivalence principle, the idea of which belongs to the authors, and often provides a neat method for finding sampling distributions. It avoids explicit integration over the sample space and the attendant Jacobian but at the expense of verifying completeness of the underlying family of densities. Fortunately, general results on completeness obviate the need for this verification in many problems involving exponential famiilies.
The proposed approach allows one to obtain results for truncated laws via the results obtained for non-truncated laws. It is much simpler than the known approaches. The examples are given to illustrate that in many situations this approach allows one to find the results for truncated laws and to estimate system reliability in a simple way.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62E15 Exact distribution theory in statistics
62N05 Reliability and life testing
62N02 Estimation in survival analysis and censored data
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