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Weighted Distributions Arising Out of Methods of Ascertainment: What Population Does a Sample Represent?

In: A Celebration of Statistics

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  • C. Radhakrishna Rao

Abstract

The concept of weighted distributions can be traced to the study of the effects of methods of ascertainment upon the estimation of frequencies by Fisher in 1934, and it was formulated in general terms by the author in a paper presented at the First International Symposium on Classical and Contagious Distributions held in Montreal in 1963. Since then, a number of papers have appeared on the subject. This paper reviews some previous work, points out, through appropriate examples, some situations where weighted distributions arise, and discusses the associated methods of statistical analysis. Weighted distributions occur in a natural way in specifying probabilities of events as observed and recorded by making adjustments to probabilities of actual occurrence of events taking into account methods of ascertainment. Failure to make such adjustments can lead to wrong conclusions.

Suggested Citation

  • C. Radhakrishna Rao, 1985. "Weighted Distributions Arising Out of Methods of Ascertainment: What Population Does a Sample Represent?," Springer Books, in: Anthony C. Atkinson & Stephen E. Fienberg (ed.), A Celebration of Statistics, chapter 0, pages 543-569, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8560-8_24
    DOI: 10.1007/978-1-4613-8560-8_24
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