A celebration of statistics, The ISI Centen. Vol., 543-569 (1985).

[For the entire collection see

Zbl 0567.00012.]
The concept of weighted distributions can be traced to the study of the effects of methods of ascertainment upon the estimation of frequencies by {\it R. A. Fisher} in 1934 [Ann. Eugen. 6, 13-25 (1934)] and it was formulated in general terms by the author in his paper ”On discrete distributions arising out of methods of ascertainment.” Sankhyā, Ser. A 27, 311-324 (1965). Since then, a number of papers has 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.