Weighted Distributions Arising Out of Methods of Ascertainment.

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. The importance of specification of the class of underlying probability distributions or stochastic model in data analysis based on a detailed knowledge of how data are obtained is emphasized. Failure to take into account the conditions of ascertainment of data can lead to wrong conclusions.